Vertex Form
What is the vertex of f(x) = (x - 2)² + 5?
(2, 5)
What is the leading coefficient a in f(x) = 2x² - 8x + 3?
a = 2
What is the greatest common factor of the terms in 6x² + 9x?
3x
Find f(0) for f(x) = x² + 4x + 6.
6
For f(x) = -3(x + 1)² + 4, state the opening direction and the vertical stretch factor.
Opens downward; vertical stretch factor 3.
Find the axis of symmetry of f(x) = x² - 6x + 4.
x = 3
Factor completely: x² + 7x + 12.
(x + 3)(x + 4)
A quadratic passes through (-2, 9). Substitute this point into f(x) = ax² + bx + c to write one equation in a, b, and c. Do not solve for the coefficients.
4a - 2b + c = 9
Write f(x) in vertex form: vertex (-2, 6), vertical stretch factor 2, opening downward.
f(x) = -2(x + 2)² + 6
Find the vertex of f(x) = x² + 4x + 1. Does the function have a maximum or minimum?
Vertex (-2, -3); minimum.
Factor completely: x² - 4x - 21.
(x - 7)(x + 3)
A ball's height is h(x) = -x² + 10x + 4 feet, where x is horizontal distance in feet from release. What is its height when x = 2?
20 feet
For f(x) = 2(x - 3)² - 8, state the axis of symmetry, minimum value, and range.
Axis of symmetry: x = 3; minimum value: -8; range: f(x) ≥ -8.
Rewrite f(x) = -2x² + 12x - 11 in vertex form.
f(x) = -2(x - 3)² + 7
Factor each completely: a. x² - 12x + 36
(x - 6)²
A ball's height is h(x) = -x² + 10x + 2 feet, where x is horizontal distance in feet from release. A 20-foot wall is 6 horizontal feet away. Find the height at the wall and how far above or below the top the ball passes.
Height: 26 feet; the ball clears the wall by 6 feet.
A quadratic has vertex (-1, 8) and passes through (1, 0). Write f(x) in vertex form, determine the vertical stretch factor, and state its domain and range.
f(x) = -2(x + 1)² + 8; stretch factor 2; domain: all real numbers; range: f(x) ≤ 8.
For f(x) = -x² - 4x + 5, find the axis of symmetry, rewrite the function in vertex form, and state the vertex and maximum value.
Axis of symmetry: x = -2; f(x) = -(x + 2)² + 9; vertex (-2, 9); maximum value 9.
Factor completely: 6x² - 7x - 3.
(3x + 1)(2x - 3)
For points (0, 5), (1, 8), and (3, 26), a student writes: a + b + c = 5; a + b + c = 8; 9a + 3b + c = 26. Correct the incorrect equation and find f(x) in standard form.
Replace the first equation with c = 5. a = 2, b = 1, c = 5, so f(x) = 2x² + x + 5.