Graphing Quadratics
The u-shaped graph shown by a quadratic.
Parabola
Factor the following expression completely.
9x + 15
3(3x+ 5)
Factor completely.
64 - 9x2
(8 + 3x) (8 - 3x)
Violet launches a toy rocket from a platform. The height of the rocket in feet is given by
h(t) = −16t2 + 64t + 80
where t represents the time in seconds after launch. What is the rocket’s initial height?
80 feet
Write the quadratic equation in standard form:
-8x - 4x2 = 14
-4x2 - 8x - 14
The highest or lowest point on the graph of a quadratic. Also known as the turning point.
Vertex.
Factor the following expression completely.
10x5 - 80x2
10x2(x3 -8)
Factor completely.
36 - x2
(6 + x) (6 - x)
Lillian kicks a football. Its height in feet is given by
h(t) = -16t2 + 72t,
where t represents the time in seconds after kick. How many seconds have gone by when the football is at its highest point?
2.25 seconds
Factor completely.
x2 + 11x +28
(x + 4) (x + 7)
Write the following quadratic function in vertex form.
y = 2x2 - 8x +5
y = 2(x-2)2 -3
Factor the following expression completely.
-45 - 50x4
-5(9 + 10x4)
Factor completely.
288 - 2x2
2(12 + x) (12 - x)
Indigo launches a toy rocket from a platform. The height of the rocket in feet is given by
h(t) = -16t2 + 80t + 96
where t represents the time in seconds after launch. What is the rocket's greatest height?
196 feet
Factor completely.
4x2 - 8x - 12
4(x + 1) (x - 3)
Write the equation for the axis of symmetry.
-x2 + 8x -7
x = 4
Factor the following expression completely.
-30x4 - 50x2
-10x2(3x2 +5)
Factor completely.
121x4 + 9y4
(11x2 + 3y2) (11x2 - 3y2)
The width of a rectangle is 2 units less than the length. The area of the rectangle is 24 units. What is the length, in units, of the rectangle?
length is 6
Solve the quadratic by factoring.
x2 + 3x - 43 = -3x -3
x = 4, x = -10
Given the quadratic equation x2 + 10x + 16.
Find the difference between the least root and greatest root.
-5
Factor the following expression completely.
x5y5 + x3y
x3y(x2y4 + 1)
Factor completely.
81 - 100x3y6
PRIME!
YOU CANNOT FACTOR
The difference of the square of a number and 54 is equal to 3 times that number. Find the negative solution.
-6
Noah was solving the following quadratic equation.
x2 - 84 = 2x - 4
He took the following steps:
x2 - 84 - 2x + 4 = 0
x2 - 2x - 80 = 0
(x - 10) (x + 2)
x = -10 x = 2
What did he do incorrectly?
Noah did not set the two factors equal to zero and solve correctly.