TOTAL
MCR 3U1-pm
TEST Chapter 3: Quadratic Functions
Name: ___________
/34
Date : _____________
1. SOLVE the following quadratic equations. Leave the answer in simplified radical form (exact answer).
a)
5x 2  2x  3  4x 2 12x
b)
1
x  22  7  16
3
2. Determine the equation of the parabola in standard form with x-intercepts
through (5, –4).
[4] [3]
, and that passes
[3]
3. Determine the base of the triangle if the area is 5 6 - 3 2 and the height is given below
Leave the answer in simplified radical form (exact answer).
[4]
4. Explain how the discriminant can help determine the number of solutions to a quadratic-linear
system of equations. Provide illustrations of these cases.
[3]
5. Describe two ways to find the vertex of a quadratic function if the equation is in standard form.
[2]
6. STL is running a ski-for-charity-trip during March Break. Last year 25 students went on this trip and
each paid $600. This year the price will increase and the research suggests that for every $20
increase in price 1 fewer student will go on the trip. The transportation, hotel and lift tickets cost
$500 per person.
a) What is the maximum profit from this trip?
b) What is the new price to maximize profit?
7. A painting is to be painted on a wall. The wall is 20 meters by 15 meters. A space of uniform width
is to surround this painting. If the painting is to cover 80% of the area of the wall, how wide must
the space be? Leave answer to one decimal place.
[3] [1]
[4]
8. A quadratic function has the following characteristics:
· x = -1 is the axis of symmetry
· x = -5 is the x-intercept
· y = -32 is the minimum value
Determine the y – intercept of the parabola.
9. Given that 𝑓(𝑥) = −2𝑘𝑥 2 − 8𝑥 − 12 − 𝑘 has one real root, find the possible value(s) of 𝑘.
Leave answer in simplified radical form.
[3]
[4]