Foundations 11 Quadratics Review

Quadratic Functions Review

• Vertex

• Roots

• Y-intercept​

​

Label the parts on your screen

Parts of the Quadratic Function

​

Vertex

• Also the Max or Min

• Always write as an ordered pair (x,y)

• When asked to write the value of the Max or Min, write the y value of the vertex

Domain & Range

• The domain will always always always always be all real numbers (-inf, inf)

• Range is the lowest point to the highest point (one of those points will always be infinity)

• y>min or y<max
  

Axis of Symmetry

• Vertical line that splits the function down the middle

• Write your answer as x = k; k is the x value of the vertex

• 
  

Multiple Choice

What is the green dot on the parabola called?

• vertex
• root
• dot
• minimum value

Multiple Choice

What is the green dashed line called?

• roots or x-intercepts
• parabola
• axis of symmetry
• line of dashes

Multiple Choice

Does this graph in the back have maximum or minimum value?

• maximum
• minimum
• neither
• both

Multiple Choice

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

• y = -2
• x = 3
• x = -3
• y = 2

x - intercepts

• Also called zeros or roots

• There can be 2, 1, or no zeros

• Write your answer as an ordered pair (x,y); y value will always be 0

Multiple Select

What are the zeros of the function? Choose all that apply.

• x = 0

• x = -3

• x = -6

• y = 18

Multiple Choice

Which answer choice describes  y = -3x² +7x - 2 accurately?

• opens up with a maximum
• opens up with a minimum
• opens down with a maximum
• opens down with a minimum 

Multiple Choice

What is another word for zeros?

• y-intercepts
• roots
• vertex
• axis of symmetry

Multiple Choice

Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t² + 96t. What is the range of the function?

• 0 ≤ y ≤ 145

• y ≤ 145

• 0 ≤ x ≤ 6

• All Reals

Multiple Choice

What are the x- intercepts?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

Multiple Choice

How many solutions does this graph have?

• one
• two
• no solutions
• cannot be determined

Multiple Choice

What is the range of this function?

• (- ∞,+∞)
• [0, +∞)
• [-2, +∞)
• [2, +∞)

Multiple Choice

What does "a" control in a graph of f(x) = ax²+ bx+ c?

• Opens up or down
• Where the graph crosses at X-intercept
• Where the graph crosses at Y-intercept

Multiple Choice

What form is the equation in?
y = 2x²-8x+7

• Standard
• Vertex
• Factored
• None of These

Multiple Choice

What is the y intercept for the equation:
y = -8x² + 3x - 7

• (0, -8)
• (0, 3)
• (0, 7)
• (0, -7)

Multiple Choice

What is the axis of symmetry for the following equation?
y=4x²-8x+9

• x=-8
• x=1
• x=-1
• x=2

Multiple Choice

Find the vertex of 
f(x) = -x² - 4x + 12

• (-2, 16)
• (2, 0)
• (2, 4)
• (-2, 4)

Multiple Choice

Which form is the equation
y = -3(x-5)²+7 in?

• Standard
• Vertex
• Factored
• None of These

Multiple Choice

What is the vertex of
f(x) = 2(x - 5)² + 12

• (-5, -12)
• (5,-12)
• (5, 12)
• (-5, 12)

Multiple Choice

Identify the vertex and whether the graph opens up or down.

• (-1, 4); opens up
• (-1, 4); opens down
• (1, 4); opens up
• (1, 4); opens down

Multiple Choice

y = 5(x+2)(x-1)

• Standard
• Vertex
• Factored
• None of These

Multiple Choice

What are the
x-intercepts of the function
f(x)= (x - 2)(x + 3)?

• x = - 2 or x = 3
• x = 2 or x = -3
• The are no real roots
• x = 2 or x = 3

Multiple Choice

If I want to find out when an object hits the ground, I should _________.

• Use x = (-b/2a) as my answer.
• Set my equation = 0 and solve.
• Replace x with 0 and evaluate.
• Find the y-coordinate of the vertex.

Multiple Choice

y = (x-9)²+5
What is the vertex? 

• (-9,5)
• (9,5)
• (5,-9)
• (-5,9)

Multiple Choice

What is the y-intercept of the following funtion
f(x) = -2x² +3x - 7

• (0, -2)
• (0, 3)
• (0, -7)
• (0, 7)

Quadratic Functions

Multiple Choice

When I want to find the maximum or minimum height of an object, I should_____.

• Set the equation = 0 and solve.
• Use x = (-b/2a) as my answer.
• Substitute x = 0 into the equation.
• Find the y-coordinate for the vertex.

Multiple Choice

What is vertex form of a quadratic function

• ax² + bx + c
• a(x - h)² + k
• y - y₁ = m(x - x₁)
• Ax + By = C

Multiple Choice

Which of these is a quadratic function?

• f(x) = 2x + 4
• f(x) = -2x + 4
• f(x) = 3x²
• q(x) = 3x³ + 2x² - 4x + 9

Find the coordinate of the vertex in the function:

-2x²+8x-2

​

​Some text here about the topic of discussion.

X- Value of the vertex: -b/2a

Multiple Choice

What is the vertex of the quadratic function:
y = x² - 6x + 11?

• (3,2)
• (-3,-2)
• (-3,2)
• (3,-2)

Transformations:

• a - how wide or narrow the graph is and if it reflects

• -h - x value of the vertex (always opposite)

• k - y value of the vertex​

​

​Some text here about the topic of discussion.

y=a(x-h)²+k

​

Multiple Choice

Does
y = -4x²
have a maximum or minimum value?

• maximum
• minimum

Multiple Choice

Describe the transformation of y = (x - 4)²

• Shift UP
• Shift DOWN
• Shift LEFT
• Shift RIGHT

Multiple Choice

Describe the transformation of y = x² + 4

• Shift UP
• Shift DOWN
• Shift LEFT
• Shift RIGHT

Multiple Choice

Compare the function y = 0.3x² to the parent function y = x²

• Wider
• Narrower

Multiple Choice

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Multiple Choice

Match the equation to its description.

• Reflected over x, right 2 and up 1
• Reflected over x, left 2 and up 1
• Reflected over x, right 2 and down 1
• Reflected over x, left 2 and down 1

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

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

• g(x)=(x+3)²
• g(x)=(x-3)²
• g(x)=x²+3
• g(x)=x²-2

Multiple Choice

Does the equation open up or down? 
Y = -3x² +7x - 2

• up
• down
• both 
• neither

Multiple Choice

Find the vertex of 
f(x) = -x² - 4x + 12

• (-2, 16)
• (2, 0)
• (2, 4)
• (-2, 4)

​Solving a Quadratic Equation

​One way to solve a quadratic equation is by factoring.

​

​Break the quadratic equation into its linear factors.

​

​Set each factor = 0 and solve.

Solve by the quadratic formula

​all quadratic equations can be solved by the quadratic formula.

​

​The part under the radical is called the discriminant.

​

​It determines the number and type of solutions that the quadratic equation has.

Multiple Choice

Use the quadratic formula to find the solutions for

y = 2x² - 9x + 5

• -8.14 and 6.14

• -4.07 and 3.07

• 3.9 and 0.6

• No solutions

Multiple Choice

How many solutions does the function have: $$-3x^2+12x-1=0$$  

• 1 solution

• 2 solutions

• No solution

• Infinite solutions

Multiple Choice

Factor
k² -2k - 24

• (k+4)(k-6)
• (k+4)(k+6)
• (k+6)(k-1)
• (k-4)(k+6)

Multiple Choice

Solve by factoring
3m² - 2m = 1

• {4/5, 3}
• {1/5, 5/2}
• {3/2, 1}
• {-1/3, 1}

Multiple Choice

Solve by square roots
5x² = 80

• {4, -4}
• {4}
• {5.831, -5.831}
• {8.185, -8.185}

Multiple Choice

Solve Using the Quadratic Formula
 x² + 4x - 40 = -8

• -10 & -4
• -4 & 10
• -8 & 4
• 8 & -4

Multiple Choice

What should you do first in solving this equation?
x² + 6x - 13 = 3

• Get factored form
• Write down: a=1, b=6, c=-13
• Make it equal 0 by subtracting 3 on each side
• Type it all in a calculator.

Multiple Choice

Solve
4m² - 100 = 0

• m=25, -25
• m=96
• m=5, -5
• m=-96

Multiple Choice

The two solutions to 
y = 2x² -x -3 are...

• 1 and 3/2
• -1 and 3/2
• -1 and -3/2
• 1 and -3/2

Multiple Choice

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing

• True
• False, because the solution and root are the same but the x-intercept and zero are different
• False, because the x-intercept and root are the same but the zero and solution are different
• False, they are all different