Vocabulary
Every quadratic equation has a U-shaped graph called this.
Parabola
A tiger's jump is recorded. The tiger's height h, in feet, after x seconds is given by the function:
y=-(x-2)2+20
What is the maximum height the tiger reaches?
20 ft
Describe how this graph looks compared to the parent function, y=ax2.
y=5x2
Narrower
Find the vertex and axis of symmetry.
y=(x-3)2+4
Vertex: (3, 4)
Axis of symmetry: x=3
Rewrite in standard form.
y=(x-4)2+4
y=x2-8x+20
The highest or lowest point on a parabola.
Vertex
Someone jumps off of a diving board. The following equation represents his dive. What was his starting height?
y=-16x2+20x+25
25 ft
Describe how this graph looks compared to the parent function, y=ax2.
y=-3x2
Narrower and faced down.
Find the vertex and axis of symmetry.
y=(x+1)2-8
Vertex: (-1, -8)
Axis of symmetry: x=-1
Rewrite in standard form.
y=(x+2)2+2
y=x2+4x+6
What form is this?
y=ax2+bx+c
Standard Form
A ball is thrown into the air. The height h, in feet, of the ball after x seconds is given by the function:
h=-x2+4x+1
What is the maximum height of the ball?
5 ft
Describe how this graph looks compared to the parent function, y=ax2.
y=-0.7x2
Wider and faced down.
Find the vertex and axis of symmetry.
y=x2-4x-5
Vertex: (2, -9)
Axis of symmetry: x=2
Rewrite in standard form.
y=-2(x-1)2-1
y=-2x2+4x-3
What form is this?
y=a(x-h)2+k
Vertex Form
Someone jumps off of a diving board. The following equation represents his dive. What was his starting vertical velocity?
y=-16x2+20x+25
20 ft/s
Describe how this graph looks compared to the parent function, y=ax2.
y=0.3x2
Wider
Find the vertex and axis of symmetry.
y=2x2+4x-6
Vertex: (-1, -8)
Axis of symmetry: x=-1
Rewrite in standard form.
y=-(x-4)2+2
y=-x2+8x-14
The line that runs through the vertex and divides the parabola in half.
Axis of Symmetry
A photo has a width of x and a length of 2x. A frame around the photo is 3 inches all the way around. Write a quadratic equation to represent the total area of the photo and the frame.
y=2x2+18x+36
Write a function that has a vertex 5 to the right of the vertex of y=(x+2)2+7
y=(x-3)2+7
Find the vertex and axis of symmetry.
y=1/2x2+3x+4
Vertex: (-3, -0.5)
Axis of symmetry: x=-3
Rewrite in standard form.
y=4(x+1)2-4
y=4x2+8x