Linear Equations
What is y= 2/3 x+ 11/3
The equation y=2x^2+8x-24 in factored form.
What is y=2(x+6)(x-2)
The vertex and direction this equation opens: h(x)=-3|x+1|-6
What is (-1,-6) and down
The transformations from y = x² to f(x) = (x + 2)² − 10.
What is shift two to the left and ten down
f(x) = 2x² − 3x + 4 and g(x) = x − 5. Find f(3).
What is f(3)=13
Solve 3x − 6y = 24 for y (write it in slope-intercept form).
y = (1/2)x − 4.
Expand f(x) = −2(x + 4)² − 3 into standard form.
What is f(x) = −2x² − 16x − 35.
Write an absolute value function with vertex (2, 5) and y-intercept (0, 6).
What is y = (1/2)|x − 2| + 5.
Rewrite f(x) = −2x² + 12x − 16 in vertex form, then describe its transformations from y = x².
f(x) = −2(x − 3)² + 2 — shift right 3, vertical stretch by 2, reflect over the x-axis, shift up 2.
Using f(x) = 2x² − 3x + 4 and g(x) = x − 5, find g(f(2)).
What is g(f(2)=1
A line passes through (4, −3) and has an x-intercept at x = 2. Write its equation in point-slope form.
What is y+3=(-3/2)(x-4)
The vertex of f(x) = x² + 2x − 15.
What is (−1, −16).
Write an absolute value function that has no x-intercepts and opens upward.
What is y=|x-4|+6
The vertex of h(x) = (x + 2)² − 10.
What is (−2, −10).
Using f(x) = 2x² − 3x + 4, find f(3) + 2f(−1).
What is 31.
Write the equation of the line with slope −3/4 and a y-intercept of −2.
What is y = −(3/4)x − 2.
A quadratic has x-intercepts (3, 0) and (−5, 0) and passes through (−2, −6). Write it in factored form.
What is y = (2/5)(x − 3)(x + 5).
The x-intercepts of g(x) = (1/2)|x − 3| − 3.
What are x = 9 and x = −3.
Given f(x) = −(x + 2)(x − 4), find the vertex using the roots.
What is Axis of symmetry x = 1; vertex is (1, 9).
Using f(x) = 2x² − 3x + 4 and g(x) = x − 5, find (f ∘ g)(−2).
What is g(−2) = −7, so f(−7) = 123.
The equation of the line through (4, −1) that is perpendicular to y = 2x + 5.
What is y = −(1/2)x + 1.
A quadratic has vertex (−3, 6) and passes through (4, −8). Write it in vertex form.
What is y = −(2/7)(x + 3)² + 6.
Find the x-intercepts of g(x) = (1/2)|x − 3| − 3.
What is x = 9 and x = −3.
Given f(x) = 3(x − 2)(x + 6), find the axis of symmetry and the vertex.
What is Axis of symmetry x = −2; vertex is (−2, −48).
Using f(x) = 2x² − 3x + 4 and g(x) = x − 5, find (g ∘ f)(0).
What is f(0) = 4, so g(4) = −1.