Vocabulary
This point is the highest or lowest point of a parabola.
What is the vertex?
Given y=2(x−1)^2+5, this is the vertex.
What is (1, 5)
Solve for the vertex: y=x^2−4x+6
(2, 2)
A ball is thrown and follows h(t)=−t^2 +4t+1. What is the maximum height?
5
A student says the vertex of y=(x−2)^2 +5 is (–2, 5). What’s wrong?
They flipped the sign wrong, it’s (2, 5).
This vertical line divides a parabola into two mirror-image halves.
What is the axis of symmetry
In the quadratic y=-3x^2 +4x-2, does it open up or down?
down
Find the y-intercept of y=−x^2+7x−3
-3
A small fountain’s water path is modeled by y=−x^2 +6x. What is the maximum height?
9
A student says y=−3x^2 +1 opens upward. What’s wrong?
The coefficient of x^2 is negative, it opens downward.
This form of a quadratic, y=a(x−h)2+k, shows the vertex clearly.
What is vertex form
For y=x^2+8x+7, the axis of symmetry is this value.
x=−4
Find the x-intercepts of y=x^2 −9
x = 3 and x = -3
A bridge arch is shaped like y=-1/2(x-2)^2 +5
5
A student finds the axis of symmetry of y=x^2+2x as x = 2. Correct it.
It should be x=–1
A parabola that opens upward has this type of extremum.
What is a minimum
Identify the direction and vertex of y=−2(x+5)^2+3.
opens down, vertex (-5, 3)
Convert to vertex form: y=x^2 +6x+10
y=(x+3)^2 +1
A toy car rolls along a parabolic ramp y=−x^2+4x. At what x-value is the top of the ramp?
x=2
A student says the range of y=(x+4)^2 −9 is “all real numbers.” Correct them.
It should be 'y' is greater than or equal to −9
This term describes the set of all possible y-values the quadratic can output.
What is the range
Give the domain and range of y=4(x−3)^2 −9
Domain: all real numbers, Range: y≥−9
A parabola has vertex (4, –2) and passes through (6, 6). Find the equation
y=2(x−4)^2 −2
A rocket’s path is h(t)=−t^2 +6t+2. When does it reach the highest point?
t=3
A student says y=2x^2 −8x+7 has x-intercepts at x = 1 and 3. Fix the mistake.
D<0, so no real x-intercepts