Review for Quadratic Functions Test MCR3UI
1) Simplify.
72 8 40 2
a) b) c) d) ( 2 3)2
6 2 5
4 3
e) 48 27 12 f) (2 3 2 5 )( 5 3 ) g)
2 3
2) Use the discriminant to find the value(s) of k such that the equation 3kx 2 4 x 2 0 has 2 equal real roots
3) a) Use a graph to represent a quadratic function that has two imaginary roots.
b) How you would use a discriminant to show that the quadratic function has two imaginary roots.
4) Solve for x using the best method
a) 9 x 2 3x 2 0 b) 6 x 2 7 17 x
c) x 2 2 x 7 0 d) 3( x 3) 2 27 0
1 2
5) Find the vertex of y x 5 x 5 by completing the square. State the maximum or minimum value for the function and when
2
it occurs.
6) A public swimming pool that is 15 metres by 20 metres needs a sidewalk of uniform width around
it. City by-law states that the area of this sidewalk must be equal to the area of the pool. What is the width of the sidewalk to 1
decimal place?
7) When priced at $30 each, a toy has annual sales of 4000 units. The manufacturer estimated that each $1 increase in cost will
decrease sales by 100 units. Find the unit price that will maximize total revenue.
8) Find the maximum product of two numbers whose sum is 22. What are the two numbers?
9) The path of a basketball shot can be modelled by the equation h = – 0.125d2 + d + 1.5, where h is the height of the basketball, in
metres, and d is the horizontal distance of the ball from the player, in metres. Place your answers on the line. (6 marks)
a) Find the maximum height reached by the ball. a) _______________
b) What is the horizontal distance of the ball from the player when
it reaches maximum height? b) ______________
c) What is the height of the ball at the moment the player releases it? c) _______________
10) The hypotenuse of a right triangle is 15cm. The sum of the other two sides is 21 cm. Find the lengths of the other two sides of the
triangle.
11) a) Determine the general equation for the quadratic family that has zeros at 3 and -6.
b) If a quadratic in this family has a y-intercept of -12, determine its equation.
1) Simplify.
72 8 40 2
a) b) c) d) ( 2 3)2
6 2 5
4 3
e) 48 27 12 f) (2 3 2 5 )( 5 3 ) g)
2 3
2) Use the discriminant to find the value(s) of k such that the equation 3kx 2 4 x 2 0 has 2 equal real roots
3) a) Use a graph to represent a quadratic function that has two imaginary roots.
b) How you would use a discriminant to show that the quadratic function has two imaginary roots.
4) Solve for x using the best method
a) 9 x 2 3x 2 0 b) 6 x 2 7 17 x
c) x 2 2 x 7 0 d) 3( x 3) 2 27 0
1 2
5) Find the vertex of y x 5 x 5 by completing the square. State the maximum or minimum value for the function and when
2
it occurs.
6) A public swimming pool that is 15 metres by 20 metres needs a sidewalk of uniform width around
it. City by-law states that the area of this sidewalk must be equal to the area of the pool. What is the width of the sidewalk to 1
decimal place?
7) When priced at $30 each, a toy has annual sales of 4000 units. The manufacturer estimated that each $1 increase in cost will
decrease sales by 100 units. Find the unit price that will maximize total revenue.
8) Find the maximum product of two numbers whose sum is 22. What are the two numbers?
9) The path of a basketball shot can be modelled by the equation h = – 0.125d2 + d + 1.5, where h is the height of the basketball, in
metres, and d is the horizontal distance of the ball from the player, in metres. Place your answers on the line. (6 marks)
a) Find the maximum height reached by the ball. a) _______________
b) What is the horizontal distance of the ball from the player when
it reaches maximum height? b) ______________
c) What is the height of the ball at the moment the player releases it? c) _______________
10) The hypotenuse of a right triangle is 15cm. The sum of the other two sides is 21 cm. Find the lengths of the other two sides of the
triangle.
11) a) Determine the general equation for the quadratic family that has zeros at 3 and -6.
b) If a quadratic in this family has a y-intercept of -12, determine its equation.
