Download MCR 3U Quadratic Functions Test

MCR 3U Quadratic Functions Test
K/U
App
Com _______
1. [K/U 3] a. Express f(x) = 3x2 - 2x + 1 in vertex form by completing the square. Show all your work.
2. [K/U 4] Given g(x) = -3(x - 4)2 + 6 :
a. State the range
b. Determine the zeros. Do not approximate.
3. [K/U 4] Express in simplest terms. Do not approximate. Show all work.
4. [K/U 4] Given h(x) =
a. Sketch h(x)
.
b. Determine the equation for h-1(x).
5. [A 2] For what values of k does k = -2(x+4) + 8 have two roots? Briefly explain your thinking.
6. [A 7] Write a sequence of transformations that would transform the quadratic function “f “ into the quadratic
function “g”. Justify all your work.
y
7
6
5
4
g
3
f
2
1
–7 –6
–5 –4
–3 –2 –1
–1
1
2
3
4
5
6
7
x
–2
–3
–4
–5
–6
–7
7. [A 3] The profit function for a new product is given by P(x) = -4x2 + 28x - 40, where x is the number sold in
thousands. How many items must be sold for the company to break even? Show an algebraic solution.
8. [A 5] The height h, in metres, of a baseball after Bill hits it with a bat is described by the function
h(t) = 0.8 + 2.9t - 4.9t2, where t is the time in seconds after the ball is struck.
a. What do you think is a reasonable domain ? Explain briefly.
b. What is the maximum height of the ball? Do not approximate.