Vertex Form
What is the vertex of the graph of
the function f(x) = x^2 + 6x + 9?
(-3,0)
Solve the equation x^2 + x = 12.
x = 3 and x = −4
Determine the number of real solutions of the system y = x^2 + 8 & y = x + 15.
2
What is the equation in vertex form of a parabola with a vertex of (−1, 8) that passes through (1, 0)?
y = −2(x + 1)^2 + 8
The path of a projectile launched from a 16-ft-tall tower is modeled by the equation y = −16x^2 + 64x + 16. Graph the equation. What is the maximum height, in feet, reached by the projectile?
80 ft
Identify the interval(s) on which the function y = x^2 − 2x − 48 is positive.
x < −6 and x > 8
Use square roots to solve the equation x^2 = −25 over the complex numbers.
x = 5i and x = −5i
Solve x^2 − 7x + 5 = 0 using the Quadratic Formula
x = 7 + √29/2 and x = 7 − √29/2
Solve −3x^2 + 2x + 4 = −x − 3 by writing a linear-quadratic system and solving using the intersection feature of a graphing calculator
x ≈ -1.11 and x ≈ 2.11
Use transformations of f(x) = x^2 to graph the following function.
h(x)=(x-3)^2+5
Shift the graph left by three units
Shift the graph up by five units
Use quadratic regression to find a quadratic equation that fits the given points.
x| 0 1 2 3
y| 6.1 71.2 125.9 89.4
y ≈ −25.4x^2 + 106.66x + 2.06
A ball is thrown from the top row of seats in a stadium. The function h(t) = −16t^2 + 64t + 80 gives the height, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?
5 seconds
Write the product (4 + i)(4 − i) in the form a + bi.
17
Solve x^2 + 3x + 4 = 0 using the Quadratic Formula.
x = −3 + i√7/2 and x = −3 − i√7/2
Write the quotient 10/1 + 2i in the form a + bi.
2-4i
A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = −5t^2 + 20t + 4 gives the height h, in meters, of the ball t seconds after it is launched. What equation can be used to tell whether the ball reaches a height of 12 m? Does the ball reach a height of 12 m?
Equation: −5t^2 + 20t + 4 = 12
Reach? Yes
Factor the expression 16x^2 + 25.
(4x − 5i)(4x + 5i)
What value(s) of b will cause 4x^2 + bx + 25 = 0 to have one real solution?
b = 20 and b = −20