Unit 8: Introduction to Quadratics Review

Unit 8: Introduction to Quadratics Review

Algebra 1B Module 4 Unit 8 Review

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

Parabola Pattern

• if a=1 then the parabola follows a standard pattern when graphed

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 point is the y-intercept?

• (-6, 0)

• (14, 0)

• (4, -60)

• (0, -50)

Multiple Choice

What is y intercept

• (2,0)

• (0,-8)

• (-8 ,0)

• (-4,0)

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

Multiple Choice

How many x-intercepts does this parabola have?

• 0

• 1

• 2

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

Multiply 3x2

• Use either area model or distribution method

• Multiply all terms together

• Combine like terms to simplify

Multiple Choice

(n² + 6n − 4)(2n − 4)

• 2n³ + 16n² − 32n + 16
• 2n³ + 8n² − 32n + 16
• 2n³ + 8n² − 12n + 16
• 2n³ + 8n² − 32n - 16

Poll

How did you feel about this Quizizz?

• It helped me a lot

• It was okay

• I struggled on it.

• I struggled on it, and would like some help.

• I did better when I took it the second time.