Geometric Properties Chapter Test
Chapter
Chapter 3
Section
Geometric Properties Chapter Test
Solutions 13 Videos

State the zeros, vertex, and equation of the axis of symmetry of the parabola at the right.

Q1

The points (-9, 0) and (19, 0) lie on a parabola.

a) Determine an equation for its axis of symmetry.

b) The y—coordinate of the vertex is -28. Determine an equation for the parabola in factored form.

c) Write your equation for part b) in standard form.

Q2

Decide, without graphing, whether each data set can be modelled by a quadratic relation. Explain how you made your decision.

Q3a

Decide, without graphing, whether each data set can be modelled by a quadratic relation. Explain how you made your decision.

Q3b

Sketch each graph. Label the intercepts and the vertex using their coordinates.

\displaystyle y = (x-6)(x + 2) 

Q4a

Sketch each graph. Label the intercepts and the vertex using their coordinates.

\displaystyle y = -(x-6)(x + 4) 

Q4b

The population, P, of a city is modelled by the equation P = 14t^2 + 820t + 42 000, where tis the time in years.

When t = 0, the year is 2008.

a) Determine the population in 2018.

b) When was population about 30 000?

Q5

Expand and simplify.

\displaystyle (3x -3)(5x + 2) 

Q6a

Expand and simplify.

\displaystyle (3x -4y)(5x + 2y) 

Q6b

Expand and simplify.

\displaystyle -5(x -4)^2 

Q6c

A toy rocket is placed on a tower and launched straight up. The table shows its height, y, in metres above the ground after x seconds.

a) What is the height of the tower?

b) How long is the rocket in flight?

c) Do the data in the table represent a quadratic relation? Explain.

d) Create a scatter plot. Then draw a curve of good fit.

e) Determine the equation of your curve of good fit.

f) What is the maximum height of the rocket?

Q7

Evaluate.

a) \displaystyle 7^{-2} 

b) \displaystyle -3^0 

a) \displaystyle -(\frac{2}{3})^{-4} 
b) \displaystyle -5^{-3}