Rewrite each relation in the form y = a(x - h)^2 + k by completing the square. Use algebra tiles or a diagram to support your solution.

\displaystyle y =x^2 + 8x -7

Rewrite each relation in the form y = a(x - h)^2 + k by completing the square. Use algebra tiles or a diagram to support your solution.

\displaystyle y = x^2 + 2x +7

Rewrite each relation in the form y = a(x - h)^2 + k by completing the square. Use algebra tiles or a diagram to support your solution.

\displaystyle y = x^2 + 4x +6

Rewrite each relation in the form y = a(x - h)^2 + k by completing the square. Use algebra tiles or a diagram to support your solution.

\displaystyle y = x^2 + 6x - 3

Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.

\displaystyle y = x^2 + 12x + 30

Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.

\displaystyle y = x^2 - 14x + 50

Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.

\displaystyle y = -x^2 + 6x - 7

Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.

\displaystyle y = 5x^2 - 40x + 76

Use a graphing calculator to find the maximum or minimum point of each parabola, rounded to the nearest tenth.

\displaystyle y = 2.1x^2 -2.5x + 8.0

Use a graphing calculator to find the maximum or minimum point of each parabola, rounded to the nearest tenth.

\displaystyle y = -338x^2+127x -212

Use a graphing calculator to find the maximum or minimum point of each parabola, rounded to the nearest tenth.

\displaystyle y = \frac{1}{5}x^2 - \frac{2}{25} x + \frac{3}{5}

Solve by factoring. Check your solutions.

\displaystyle x^2 + 10x + 21 = 0

Solve by factoring. Check your solutions.

\displaystyle m^2 + 8m, - 20 = 0

Solve by factoring. Check your solutions.

\displaystyle 6y^2 + 21y + 9 = 0

Solve by factoring. Check your solutions.

\displaystyle 5n^2 + 13n - 6 = 0

Solve.

\displaystyle y^2 = 8y + 9

Solve.

\displaystyle x^2 - 8x = - 7

Solve.

\displaystyle 3m^2 = -10m - 7

Solve.

\displaystyle 30x -25x^2 = 9

Solve.

\displaystyle 8k^2 = -5 + 14k

Solve.

\displaystyle 3x^2 + 2 = -5x

The length of the hypotenuse of a right triangle is 1 cm more than triple that of the shorter leg. The length of the longer leg is 1 cm less than triple that of the shorter leg. Find the lengths of the three sides of the triangle.

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

\displaystyle y = x^2 +8x + 12

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

\displaystyle y = x^2 -4x -5

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

\displaystyle y = -x^2 -6x + 27

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

\displaystyle y = 3x^2 + 10x + 8

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

\displaystyle y = -x^2 - 3x

Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.

\displaystyle y = x^2 -4

If two different quadratic relations have the same zeros, will they necessarily have the same axis of symmetry? Will they have the same vertex? Explain your reasoning.

Find the value(s] of k so that the parabola has only one x-intercept.

\displaystyle y =x^2 + kx + 100

Find the value(s] of k so that the parabola has only one x-intercept.

\displaystyle y = -4x^2 + 28x + k

Use the quadratic formula to solve the equation. Express your answers as exact roots.

\displaystyle -3x^2 + 2x + 5 = 0

Use the quadratic formula to solve the equation. Express your answers as exact roots.

\displaystyle 9x^2 -8x -3 = 0

Use the quadratic formula to solve the equation. Express your answers as exact roots.

\displaystyle 5x^2 + 7x + 1 = 0

Use the quadratic formula to solve the equation. Express your answers as exact roots.

\displaystyle 25x^2 + 90x + 81 = 0

If a baseball is batted at an angle of 35° to the ground, the distance the ball travels can be estimated using the equation d = 0.0034s^2 + 0.004s - 0.3, where sis the bat speed, in kilometres per hour, and d is the distance flown. in metres. At what speed does the batter need to hit the ball in order to have a home run where the ball flies 125 m? Round to the nearest tenth.

A d1ver bounces off a 3-m springboard at an initial upward speed of 4 m/s.

a) Create a quadratic model for the height of the diver above the water.

b) After how many seconds does the diver enter the water? Round to the nearest hundredth of a second.

c) Over what time interval is the height of the diver greater than 3.5 m above the water? Round to the nearest hundredth of a second.

A rectangular garden measures 5 m by 7 m. Both dimensions are to be extended at both ends by the same amount so that the area of the garden is doubled. By how much should the dimensions increase. to the nearest tenth of a metre?

The Sticker Warehouse sells rolls of stickers for $4.00 each. The average customer buys six rolls of stickers. The owner finds that, for every $0.25 decrease in price. the average customer buys an additional roll.

a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent The Sticker Warehouse's total revenue per customer.

b) With how many price reductions will the revenue per customer be $30?

c) What is the maximum predicted sales revenue per customer? With how many price reductions will this occur?