Factoring and solving Quadratics
Factor the following quadratic
x2 - 16
(x+4)(x-4)
What is the vertex, axis of symmetry, domain, and range in the following quadratic function?
f(x) = 2(x + 5)2 - 2
vertex: (-5, -2)
axis of symmetry: x = -5
domain: all reals
range [-5, ∞)
Describe the transformations being applied to the parent function f(x) = √x
f(x) = 2√x - 4
Graph stretches vertically by factor of 2 and translates 4 units down
If f(x) = x + 2
and g(x) = x + 5
2x + 7
Factor the following quadratic
x2 + 9x + 20
(x+4)(x+5)
Find the x and y intercepts of the following quadratic.
f(x) = x2 - 10x + 16
y int: (0,16)
x int: (2,0) and (8,0)
Solve the following radical equation.
∛(x-2) = 2
If f(x) = g(x) = x + 3
What is (f · g)(x)
x2 + 6x + 9
Factor the following Quadratic in simplest form
4x2 - 20x + 24
4(x - 3)(x - 2)
Convert the following quadratic from vertex form to standard form.
f(x) = 2(x - 5)2 + 7
f(x) = 2x2 - 20x + 57
Solve the following radical equation
√(5-x) = √(2x - 1)
2
If f(x) = x + 6
and g(x) = x2 - 4x + 11
what is (f/g)(x)
(x + 6)/ x2 - 4x + 11
Solve the following quadratic equation.
x2 + 2x + 9 = 0
x = -1 ± i√8
Write the equation of the quadratic that has vertex (3,8) and goes through the point (7,9)
f(x) = (1/16)(x - 3)2 + 8
Given the vertex of a radical function is (4,6) and a point is (5,5) write the radical function in standard form.
f(x) = - sqrt(x-4) + 6
If f(x) = x2 + 8x + 3
and g(x) = x + 7
what is ( f ∘ g)(x)
x2 + 22x + 108
Factor the following trinomial
3x2 + 8x + 5
Convert the following quadratic from standard from to vertex form.
f(x) = x2 + 14x - 12
f(x) = (x + 7)2 - 61
solve the following radical equation
√(3x) = - √12
no solution
If f(x) = x2 + 2x + 6
and g(x) = x + 4
What is ( f ∘ g)(2)
54