Quadratic Function Review

Quadratic Function Review

Key features, graphing, equations and transformations

Key Features of Standard Form

• 'a' value determines how parabola opens

• 'c' value is the y-intercept

• Axis of Symmetry Equation -

   $x=\frac{-b}{2a}$  

• Use x value to find y value of vertex

Multiple Choice

Which way does the parabola open?

y = 3x²- 6x + 4

• up

• down

Multiple Choice

What's the y-intercept of y = 3x²- 6x + 4

• (4,0)
• (-4,0)
• (0,-4)
• (0,4)

Multiple Choice

What is the axis of symmetry of y=2x²-4x+9?

• x = 1
• x = -1
• x = -2
• x = 4

Multiple Choice

What is the vertex of y=x²+4x+3?

• (2,1)
• (-2,1)
• (0,0)
• (-2,-1)

Key features from Graph

• Vertex - high or low point

• Maximum - when vertex is the high point

• Minimum - when vertex is the low point

• Domain - Left to Right (x-axis)

• Range - low to high (y-axis)

Multiple Choice

Does the graph of this equation open up or down? 
f(x) = -(x + 3)² - 5

• up
• down

Multiple Choice

Which of the statements about the graph is FALSE?

• The vertex is a maximum

• There are two zeros at x = -3 and x = 3

• The y-intercept is (0, 18)

• The range is y ≥ 18

Multiple Choice

What is the vertex?

• (-3, 0)

• (3, 0)

• (0, 18)

• (18, 0)

Multiple Choice

State the domain and range.

• Domain: All real numbers, Range: y ≥ -9

• Domain: All real numbers, Range: All real numbers

• Domain: x ≥ -8, Range: y ≥ -9

• Domain: x ≥ -8, Range: All real numbers

Vertex Form

• Vertex (h,k)

• When pulling out a coordinate - h is the opposite sign

• Axis of symmetry - x=h, opposite sign

Multiple Choice

Given the equation y = 3(x + 5)² - 4,

what is the axis of symmetry?

• x=5

• x=-5

• x=4

• x=-4

Multiple Choice

Given the equation y = 3(x + 5)² - 4,

what is the vertex of the parabola?

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Transformations from Vertex Form

• a - shows stretch/dilation and reflection

• h - positive = left and negative = right

• k - positive = up and negative = down

Vertex Form

• Vertex - (2,1)

• Axis of Symmetry - x=2

• Reflected over x-axis, compressed by 3/4

• Right 2

• Up 1

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

What steps transform the graph y = x² to y = -1/2(x-4)² + 1?

• Compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

• Stretched by 1/2, shifted 4 units right and 1 unit down

Factored Form

• The x-intercepts are in parentheses

• OPPOSITE sign

• points are (-3,0) and (2,0)

• Other names for x-intercepts are zeros and roots

• 
  

Multiple Choice

What are the

x-intercepts of the function

f(x)= (x - 2)(x + 3)?

• (-2,0) and (3,0)

• (2,0) and (-3,0)

• (0,2) and (0,3)

• (0,-2) and (0,3)

Quadratic Tables

• Look for 2nd difference

• Find how y changes, then how those values change

Multiple Choice

What is the 2nd difference?

• -3

• -2

• 2

• 3