A2 Final Exam Review 22-23 S1 (Pt. 1)

Algebra 2 CP Final Exam Review, Pt. 1

Topic: Everything Quadratics

This assignment counts as a minor grade. Please complete it twice if your first grade is unsatisfactory.

Quadratics

• y=x²

• Quadratic functions form a "u" shaped graph called a parabola

Multiple Choice

What kind of function creates a parabola?

• Linear

• Cubic

• Absolute Value

• Quadratic

Parent Function

• All quadratics are based off of the parent function y=x²

Vertex

• The turning point or tip of our parabola

• The vertex is either a maximum or minimum depending on the direction of our parabola

Multiple Choice

What is vertex

• (-9,-1)

• (1,-9)

• (-1,-9)

• (0,-9)

Multiple Choice

What is the vertex

• (-1, 7)

• (7 , -1)

• (0, 5)

• (-1, -7)

Axis of Symmetry

• Goes through the center of the parabola

• Always goes through the vertex

• x=h or x=-b/2a

Multiple Choice

What is the axis of symmetry

• x = -8

• y = -1

• x = -1

• y = -8

Multiple Choice

What is the axis of symmetry?

• y = -4

• y = 1

• x = 1

• x = -4

Y-Intercept

• Point that touches/crosses the y-axis

• X-coordinate is 0

Multiple Choice

What is y intercept

• (2,0)

• (0,-8)

• (-8 ,0)

• (-4,0)

Multiple Choice

What point is the y-intercept?

• (-6, 0)

• (14, 0)

• (4, -60)

• (0, -50)

X-Intercept(s)

• Point(s) that touches/crosses the x-axis

• Y-coordinate is 0

• Also known as zeros or solutions

Multiple Choice

What are the x intercepts

• (-4, 0) and (2,0)

• (0,-4) and (0,2)

• (-4 ,0) and (-2,0)

• (4,0) and (2,0)

X-Intercept(s)

• If the vertex is below the x-axis, there will be two x-intercepts

• If the vertex is on the x-axis, there will be one x-intercept

• If the vertex is above the x-axis, there will be no x-intercepts

Standard Form

• Standard Form is a trinomial

• The most visible point while in standard form is the y-intercept

• We can use the formula x=-b/2a to find the axis of symmetry

• We can use this to also find the x-coordinate and y-coordinate of our vertex

Multiple Choice

What is the standard form of a quadratic function?

• y=mx+b

• y=a(x-h)²+k

• f(x)=ax²+bx+c

• f(x)=(x+a)(x-b)

Multiple Choice

What is the axis of symmetry?

y= 3x² + 12x -5

• 6

• -6

• 2

• -2

Multiple Choice

What is the y-intercept of y=x²-6x+7

• (1,-6)

• (0,7)

• (7,0)

• (-6, 1)

Vertex Form

• Vertex form is written as a binomial term squared plus an integer

• We can easily see our vertex in vertex form

Multiple Choice

What is the vertex form of a quadratic function?

• y=mx+b

• y=a(x-h)²+k

• f(x)=ax²+bx+c

• f(x)=(x+a)(x-b)

Multiple Choice

What is the vertex of the equation

$$y=\left(x+7\right)^2+3$$  

• (7, 3)

• (7, -3)

• (-7, 3)

• (-7, -3)

Direction

• If a is positive (+) then it is CONCAVE UP (smiling) and has a MINIMUM

• If a is negative (-) then it is CONCAVE DOWN (frowning) and has a MAXIMUM

Multiple Choice

Is the "a" positive or negative?

• positive

• negative

Multiple Choice

Does this open upwards or downwards?
y= -3x² + 6x - 6

• up

• down

Multiple Choice

Does this graph have a maximum or minimum?

• Minimum

• Maximum

Multiply 2x2

• Use either area model or distribution method

• Multiply all terms together

• Combine like terms to simplify

Multiple Choice

Which is equivalent to (x-5)(x+6)?

• x² + x -30

• x² -x +30

• x²-5x+6

• x² -11x -30

Multiple Choice

(x − 3)(6x − 2)

• 6x² − 20x + 6

• 6x² + 20x - 6

• 6x² +6

• 6x + 6

​

​

Multiple Choice

To factor $$x^2-8x-20$$   I am looking for a pair of numbers that _________

• have a product of -20 and a sum of -8

• have a product of -8 and a sum of -20

• have a product of 20 and a sum of 8

• have a product of 8 and a sum of 20

Multiple Choice

Factor: $$x^2+4x+3$$  

When looking for the two integers:

which integer pair combination needs to be met?

• Product is 3

  Sum is 4 

• Product is 4

  Sum is 3

Multiple Choice

What equations would I use to solve x² + 14x - 32 =0

• x + 16 = 0

  and x - 2 = 0

• x + 7 = 0

  and

  x - 7 = 0

• x - 16 = 0

  and

  x + 2 = 0

• x² + 14 = 0

  and

  x - 32 = 0

Multiple Choice

Factor the following quadratic expression:

x² + 6x + 9

• (x+3)(x-3)

• (x-3)(x-3)

• (x+3)(x+3)

• (x-3)(x-3)

Multiple Choice

Which of the following is a factor of x²-10x+24?

• x-4

• x+4

• x+6

• x-2

Multiple Choice

Convert x² - 9x + 20 = 0 to factored form and solve.

• (x-10)(x+2)=0

  x = -2, 10

• (x+4)(x+5)=0

  x = -5, -4

• (x-4)(x-5)=0

  x = 4, 5

• Not factorable

Multiple Choice

$$3x^2-10x+1=0$$  

Solve using the quadratic formula. Leave your answer in exact form.

• $$x=\frac{-10\pm\sqrt{88}}{6}$$  

• $$x=\frac{-5\pm2\sqrt{22}}{3}$$  

• $$x=\frac{10\pm\sqrt{112}}{6}$$  

• $$x=\frac{5\pm\sqrt{22}}{3}$$  

Multiple Choice

Solve Using the Quadratic Formula

x² + 4x - 40 = -8

• -10 & -4

• -4 & 10

• -8 & 4

• 8 & -4

Multiple Choice

Describe the graph of the function $$n\left(x\right)\ =\ 2x^2$$   is related to the graph of $$f\left(x\right)\ =\ x^2$$  

• n(x) is compressed vertically from f(x).

• n(x) is translated 2 units up from f(x).

• n(x) is stretched vertically from f(x).

• n(x) is stretched horizontally from f(x).

Multiple Choice

Describe how the graph of

$$b\left(x\right)\ =\ \frac{1}{2}x^2\ -\ 4$$   is related to the graph $$f\left(x\right)\ =\ x^2$$

• b(x) is stretched vertically and translated 4 units down from f(x).

• b(x) is compressed vertically and translated 4 units down from f(x).

• b(x) is stretched horizontally and translated 4 units up from f(x).

• b(x) is stretched horizontally and translated 4 units down from f(x).

Multiple Choice

Which equation would shift the quadratic function

$$f\left(x\right)=x^2$$ up 3 units and to the right 4 units.

• $$f\left(x\right)=\left(x+3\right)^2+4$$  

• $$f\left(x\right)=3\left(x-4\right)^2$$  

• $$f\left(x\right)=\left(x-4\right)^2+3$$  

• $$f\left(x\right)=\left(x+4\right)^2+3$$  

Multiple Choice

Describe the transformation:

$$f\left(x\right)=\left(x+3\right)^2-2$$  

• right 3, down 2

• up 3, left 2

• left 3, up 2

• left 3, down 2

Multiple Choice

If the blue is f(x)=x^2, then the red must be

• g(x)=x² - 5

• g(x)=x² + 5

• g(x)=(x - 5)²

• g(x)=(x + 5)²

Multiple Choice

The equation of red graph is y = x². What is the equation of the blue graph?

• y = (x + 2)² + 3

• y = 3(x + 2)²

• y = (x - 2)² + 3

• y = (x + 2)² - 3

Let's use Desmos to analyze and evaluate Quadratic Application Functions.

​

Quadratic Application Problems

Make sure you can find the following on your graph. The next 3 slides will ask for this information.

• y-intercept (starting height)

• Vertex (time, max height)

• x-intercept (time, on the ground)​

Multiple Choice

What is the initial height of the object?

• 22

• 48

• 16

• 0

Multiple Choice

How long did it take to reach the max height?

• 12 seconds

• 58 seconds

• 3.5 seconds

• 1.5 seconds

Multiple Choice

How long was the object in the air?

• 2.8 seconds

• 3.4 seconds

• 1.5 seconds

• 8 seconds

Multiple Choice

A raft is dropped from a helicopter 256 feet in the air above the ocean.  Its approximate height, h, after t seconds is given by the function h(t) = -16t² + 256.  How many seconds did it take the raft to hit the water? 

• -4

• 2

• 4

• 8

Multiple Choice

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25

Multiple Choice

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high are the fireworks after 1 second?

• 136

• 96

• 168

• 210

• 210.25

Multiple Choice

Which one are we looking for?

Elliot wants to know how high the soccer ball will get if he kicks it straight up in the air.

• x at vertex

• y at vertex

• positive zero

• y-intercept

Multiple Choice

Which one are we looking for?

Darrell is trying to find out how many seconds it will take a golf ball to get to its highest point after being hit on the golf course.

• x at vertex

• y at vertex

• positive zero

• y-intercept

Multiple Choice

Which one are we looking for?

Jaiden wanted to know the initial height of a baseball when it was hit at home plate.

• x at vertex

• y at vertex

• positive zero

• y-intercept

Multiple Choice

What should the selling price be in order to maximize profit?

• 35

• 60

• 10

• 0

Multiple Choice

What is the initial (starting) height of an object following this path? 

h(t) = -16t² +20t + 6

• -16 feet 

• 0 feet

• 20 feet 

• 6 feet