Graphing Quadratic Functions

Vocabulary

100

What is the name for a U-shaped graph of the quadratic equation?

Parabola

200

What do we call the highest or lowest point on a parabola?

Vertex

300

What is the name of the form for this quadratic equation? f(x) = ax² +bx + c

Standard form

400

When the vertex is in the lowest part of the parabola, what is it called?

The minimum

500

How do we call the line that runs through the vertex and divides the parabola in half.

Axis of symmetry

Misc.

100

What can the sign of the coefficient of an "a" term tell you about the behavior of the parabola?        f(x)= ax² +bx + c

The 'a' term tells you whether the parabola is opens upward or downward.

200

Where is the y-intercept located? How does this coordinate point look (  ,  )?

The point where the parabola crosses through the y-axis. (0,#)

300

Name the x-intercepts. Give points where the parabola is crossing the x-axis. f(x)=x^2-5x+6

(3,0) and (2,0)

400

What can the coefficient of an "a" term tell you about the behavior of the parabola? f(x)=ax² +bx + c

Positive a means opens up

Negative a means opens down

Larger number, skinnier parabola

Smaller number 0<|a|<1 wider parabola

500

List all of the steps you need to graph a quadratic in standard form.

Step 1: AOS

Step 2: Find Vertex

Step 3: Y-intercept

Step 4: Make table of values with vertex in the middle

Step 5: Graph

Axis of Symmetry

100

What does the axis of symmetry do visually?

The axis of symmetry cuts the parabola in half.

200

What is the formula for the axis of symmetry give the quadratic equation is in Standard Form?

x=-b/2a

300

What is the axis of symmetry for this quadratic function? f(x)=x² + 4x + 4

x=-2

400

What is the axis of symmetry for this quadratic function? y=-6x² -6x +9

x=-1/2

500

What is the axis of symmetry for this quadratic function? f(x)=-7x²-21x+33

x = -3/2

Graph/Writing Equations

100

Graph the following function: f(x)=x^2+4x+5

Determine the AOS, Vertex, and if the Vertex is a Max or Min.

AOS:x=-2

Vertex:(-2,1)

Min

200

Graph the following Function: f(x)=2x²-4x-3

Determine the AOS, Vertex, and if the Vertex is a Max or Min.

AOS:x=-1

Vertex:(-1,3)

Min

300

Graph the following Function: g(x)=-2x^2+10x

Determine the AOS, Vertex, and if the Vertex is a Max or Min and the X-intercept(s).

AOS:x=5

Vertex:(5,0)

Max

(0,0) (5,0)

400

A cannonball is shot and has the path it follows is given by the function. f(x)=-16x^2+96x. What is the max height of the cannonball?

144 feet

500

A superhero is trying to leap over a tall building. The function f(x)=-16x^2+200x give the superhero's height in feet as a function of time. The building is 612 feet high. Will the superhero make it over the building?

Yes, the highest the superhero jumps is 625 feet. Therefore he will make it over the building.