Write the equations of two different quadratic relations that match each description.

The graph has a narrower opening than the graph of y=2x^2

Write the equations of two different quadratic relations that match each description.

The graph has a wider opening than the graph of y =-0.5x^2

Write the equations of two different quadratic relations that match each description.

The graph opens downward and has a narrower opening than the graph of y = 5x^2.

The point (p, q) lies on the parabola y = ax^2. If you did not know the value of a, how could you use the values of p and q to determine whether the parabola is wider or narrower than y = x^2?

Match each translation with the correct quadratic relation.

a) 3 units left, 4 units down

b) 2 units right, 4 units down

c) 5 units left

d) 3 units right, 2 units up

• i) y = (x - 3)^2 + 2
• ii) y = (x + 3)^2 - 4
• iii) y = (x - 2)^2 - 4
• iv) y = (x + 5)^2

Which equation represents the graph shown? Explain your reasoning.

• a) y = -3(x + 3)^2 + 8
• b) y = -3(x - 3)^2 + 8
• c) y = 3(x - 3)^2 -8
• d) y = -2(x - 3)^2 +8

The parabola y = x^2 is transformed in two different ways to produce the parabolas y=2(x-4)2^+5 and y =2(x-5)^2+4. How are these transformations the same, and how are they different?

We rotated the parabola y = x^2 by 180° around a point. The new vertex is (6, -8). What is the equation of the new parabola?

Rick used transformations to graph y = -2(x - 4)^2 + 3. He started by reflecting the graph of y = x^2 in the x-axis. Then he translated the graph so that its vertex moved to (4, 3). Finally, he stretched the graph vertically by a factor of 2.

a) Why was Rick's final graph not correct?

b) What sequence of transformations should he have used?

c) Use transformations to sketch y = -2(x -4)^2 +3 on grid paper.

Use the point marked on each parabola, as well as the vertex of the parabola, to determine the equation of the parabola in vertex form.

Use the given information to determine the equation of each quadratic relation in vertex form.

vertex at (-3, 2), passes through (-1, 4)

Use the given information to determine the equation of each quadratic relation in vertex form.

vertex at (1, 5), passes through (3, -3)

A farming community collected data on the effect of different amounts of fertilizer, x, in 100 kg/ha, on the yield of carrots, y, in tonnes. The resulting quadratic regression model is y = -0.5x^2 + 1.4x + 0.1. Determine the amount of fertilizer needed to produce the maximum yield.

A local club alternates between bands and booking DJs. By tracking receipts over a period of time, the owner of the club determined that her profit from a live band depended on the ticket price. Her profit, P, can be modelled using P = -15x2 + 600x + 50, where x represents the ticket price in dollars.

a) Sketch the graph of the relation to help the owner understand this profit model.

b) Determine the maximum profit and the ticket price she should charge to achieve the maximum profit.

Write each quadratic relation in vertex form using an appropriate strategy.

\displaystyle y = x^2 -6x- 8

Write each quadratic relation in vertex form using an appropriate strategy.

\displaystyle y = -2(x+ 3)(x -7)

Write each quadratic relation in vertex form using an appropriate strategy.

\displaystyle y = x(3x + 12) + 2

Write each quadratic relation in vertex form using an appropriate strategy.

\displaystyle y = -2x^2 + 12x - 11

The height, h, of a football in metres t seconds since it was kicked can be modelled by \displaystyle h = -4.9t^2 + 22.54t + 1.1

a) What was the height of the football when the punter kicked it?

b) Determine the maximum height of the football, correct to one decimal place, and the time when it reached this maximum height.