Vocab
What is the name of the point on a quadratic function that will be the maximum or minimum of the function?
Vertex
What does the 'c' value tell us?
The y-intercept
Without using any math, what is the y-intercept of the function y=3x^2-5x
(0, 0)
Solve: x^2=484
Round to nearest tenth if needed
x=22
x=-22
Mia tosses a ball to her dog. The function h=-0.5t^2+2t+6 represents the path of the ball where h represents the height in feet and x represents time in seconds. What is the maximum height the ball reaches?
8 feet
What are the three other names for solutions of a quadratic equation?
Zeros, roots, x-intercepts
Without finding it, would the vertex of this function be a minimum or maximum and why? y=5x^2+10x-2
Minimum because the parabola opens up
Find the vertex of the quadratic function y=x^2+10x+6
(-5, -19)
Solve: n^2-7n=-6
Round to nearest tenth if needed
n=6
n=1
The length of a photograph is 1 cm less than twice the width. The area is 45 cm squared. Find the dimensions of the photograph.
9 cm by 5 cm
What is the name of the line that divides a quadratic function exactly in half?
Axis of symmetry
Order the following quadratic functions from narrowest to widest.
y=-10x^2 y=-1/3x^2
y=-2/3x^2 y=2x^2
y=-10x^2, y=2x^2, y=-2/3x^2, y=-1/3x^2
Graph: y=-2x^2-16x-35
V (-4, -3)
(-5, -5,)
(-3, -5)
(-6, -11)
(-2, -11)
Solve: r^2-5r-43=-9
Round to nearest tenth if needed
r=8.8
r=-3.8
A football is punted into the air. Its height h, in meters, after t seconds is modeled by the equation h=-4.9t^2+24.5t+1. When does the football hit the ground? Round to the nearest hundredth.
5.04 seconds
What are the five methods of solving a quadratic equation?
Graphing, square roots, factoring, completing the square, quadratic formula
If the x-intercepts of a quadratic function are (6, 0) and (-12, 0), what is the AOS?
AOS: x=-3
Graph: y=-2(x+2)(x-4)
V (1, 18)
(0, 16)
(2, 16)
(3, 10)
(-1, 10)
Solve the system:
y=x^2-4x-1
x+y=-3
Round to nearest tenth if needed
(1, -4) and (2, -5)
A rectangular lawn measuring 8 m by 4 m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165 m squares. What is the width of the flower bed?
3.5 m
What are the three forms of a quadratic equation?
Standard form, intercept form, vertex form
How can you transform y=x^2 to be wide, shift 5 units down, and 2 units left?
y=1/4(x+2)^2-5
Graph: y=2(x-7/2)^2+1/2
V (3.5, 0.5)
(3, 1)
(4, 1)
(2, 5)
(5, 5)
Solve: (x-3)^2=2x-1
Round to nearest tenth if needed
x=4-rt(6)=1.5
x=4+rt(6)=6.4
A rectangle and square have the same area. The length of the rectangle is 70 ft more than two times its width. The length of a side of the square is 30 ft. What are the dimensions of the rectangle?
90 ft by 10 ft