Graphing Quadratics in Standard Form

Describe the transformations from f(x)=x² to g(x)=1/4x²+4

• Reflected across x axis, up 4 units

• Vertical shrink by 1/4, up 4 units

• Vertical stretch by 4, up 4 units

• Vertical string by 1/4, left 4 units

Changing the c value of a standard form quadratic (y=ax²+bx+c) transforms the graph how?

• Up and down

• Left or right

• Reflects over x axis

• Up only

• Creates a change in the universe that is so chaotic it creates a new galaxy

Which function's graph is the result of shifting the graph of f(x)=-x²-4 3 units down?

• g(x)=-x²-1

• g(x)=-4x²-4

• g(x) = -1/3x²-4

• g(x)=-x²-7

• The parabola is concave down because a > 0.

• The parabola is concave down because a < 0

• The parabola is concave up because a < 0

• The parabola is concave up because a > 0

If we have the equation here, can we graph and match?

(a)  

• F

• G

• H

• J

Looking at the graph,

The vertex is at Point ​ (a)  

The Positive Zero is at Point ​ (b)  

The y-intercept is at Point ​ (c)  

The Negative Zero is a Point ​ (d)  

• 3

• 4

• 2

• 1

• Not Shown

The graph of quadratic function f is shown on the grid.

Vertex: (a)  

y-intercept: (b)  

Axis of Symmetry: ​ (c)  

Minimum Value: (d)  

• (-3, -5)

• (0, 4)

• x = -3

• -5

• (-2, -4)

• (-6, 4)

• (4, 0)

• 4

• x = -5

• -4

The graph of quadratic function f is shown on the grid.

f(x) = (x + 3)² − 5

Vertex: (a)  

y-intercept: (b)  

Axis of Symmetry: ​ (c)  

Minimum Value: (d)  

• (-3, -5)

• (0, 4)

• x = -3

• -5

• (-2, -4)

• (-6, 4)

• (4, 0)

• 4

• x = -5

• -4

Standard form of a quadratic equation

• y=x²

• y=ax²+bx+c

• y=mx+b

• y=x

Label the following in the graph:

a

b

d

c

e

root/x-intercept right

root/x-intercept left

vertex

axis of symmetry (AOS)

y-intercept