Solve the quadratic equation.

\displaystyle x^2 + 4x = 12

Solve the quadratic equation.

\displaystyle x^2 + 8x + 9 = 0

Solve the quadratic equation.

\displaystyle x^2 -9x = -4

Solve the quadratic equation.

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

Solve the quadratic equation.

\displaystyle 2x^2 - 5x + 10 = 15

Solve the quadratic equation.

\frac{1}{2}x^2 + 10x - 2 = -10

Determine the root(s).

\displaystyle x^2 + 6x - 16 = 0

Determine the root(s).

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

Determine the root(s).

\displaystyle x^2 + 3x - 10 = 0

Determine the root(s).

\displaystyle 6x^2 + 7x - 5 = 0

Determine the root(s).

\displaystyle -3x^2 -9x + 12 = 0

Determine the root(s).

\displaystyle \frac{1}{2}^2 + 6x + 16 = 0

Solve using any strategy.

\displaystyle x^2 + 12x + 45 = 0

Solve using any strategy.

\displaystyle 2x^2 + 7x + 5 = 9

Solve using any strategy.

\displaystyle x(6x -1) = 12

Solve using any strategy.

\displaystyle x(x + 3) - 20 = 5(x + 3)

Kate drew this sketch of a small suspension bridge over a gorge near her home.

She determined that the bridge can be modelled by the relation y = 0.1x^2 - 1.2x + 2. How wide is the gorge, if 1 unit on her graph represents 1 m?

If a ball were thrown on Mars, its height, h, in metres, might be modelled by the relation h = -1.9t^2 + 18t + 1, where tis the time in seconds since the ball was thrown.

a.Determine when the ball would be 20 m or higher above Mars’ surface.

b. Determine when the ball would hit the surface.

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle x^2 + 8x + c

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle x^2 - 10x + c

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle x^2 + 5x + c

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle x^2 - 7x + c

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle -4x^2 + 24x + c

Determine the value of c needed to create a perfect-square trinomial.

\displaystyle 2x^2 -18x + c

Write each relation in vertex form by completing the square.

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

Write each relation in vertex form by completing the square.

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

Write each relation in vertex form by completing the square.

\displaystyle y = 2x^2 + 16x + 30

Write each relation in vertex form by completing the square.

\displaystyle y = -3x^2 -18x - 17

Write each relation in vertex form by completing the square.

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

Write each relation in vertex form by completing the square.

\displaystyle y = -3x^2 + 9x -2

Consider the relation y = -4x^2 + 40x - 91.

a. Complete the square to write the equation in vertex form.

b. Determine the vertex and the equation of the axis of symmetry.

c. Graph the relation.

Martha bakes and sells her own organic dog treats for \$15/kg. For every \$1 price increase, she will lose sales. Her revenue, R, in dollars, can be modelled by y = -10x^2 + 100x + 3750, where x is the number of \$1 increases. What selling price will maximize her revenue?

For his costume party, Byron hung a spider from a spring that was attached to the ceiling at one end. Fern hit the spider so that it began to bounce up and down. The height of the spider above the ground, b, in centimetres, during one bounce can be modelled by h = 10h^2 -40t+240, where t seconds is the time since the spider was hit. When was the spider closest to the ground during this bounce?