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

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.

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

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

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

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

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

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

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?

Expand and simplify.

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

Expand and simplify.

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

Expand and simplify.

\displaystyle -5(x -4)^2

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?

Evaluate.

a) \displaystyle 7^{-2}

b) \displaystyle -3^0

Evaluate.

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

b) \displaystyle -5^{-3}