State whether each relation is quadratic.

a) y = 4x - 5

b) when

• x = -3, -2, -1, 0, 1, 2, 3,
• y = 56,35, 18, 5, -4, -9, -10 respectively

c) y = 2x (x - 5)

d)

Discuss how the graph of the quadratic relation y = 4x^2 + bx + 6 changes as a, b, and c are changed.

Find

• i. the equation of the axis of symmetry
• ii. the coordinates of the vertex
• iii. the y-intercept
• iv. the zeros

for

\displaystyle y = x^2 -8x

Find

• i. the equation of the axis of symmetry
• ii. the coordinates of the vertex
• iii. the y-intercept
• iv. the zeros

for

\displaystyle y = x^2 + 2x - 15

The x-intercepts of a quadratic relation are -2 and 5, and the second differences are negative.

a. Is the y-value of the vertex a maximum value or a minimum value? Explain.

b. Is the y-value of the vertex positive or negative? Explain.

c. Calculate the x-coordinate of the vertex.

Use graphing technology to graph the parabola for each relation below. Then determine

• i) the x—intercepts
• ii) the equation of the axis of symmetry
• iii) the coordinates of the vertex

\displaystyle y = -x^2 + 18x

Use graphing technology to graph the parabola for each relation below. Then determine

• i) the x—intercepts
• ii) the equation of the axis of symmetry
• iii) the coordinates of the vertex

\displaystyle y = 6x^2 + 15x

What does a in the equation y = ax^2 + bx + c tell you about the parabola?

The Rudy Snow Company makes custom snowboards. The company’s profit can be modelled with the relation \displaystyle y = -6x^2 + 42x - 60 , where x is the number of snowboards sold (in thousands) and y is the profit (in hundreds of thousands of dollars).

a. How many snowboards does the company need to sell to break even?

b. How many snowboards does the company need to sell to maximize their profit?

The x-intercepts of a parabola are -2 and 7, and the y-intercept is -28.

a) Determine an equation for the parabola.

b) Determine the coordinates of the vertex.

The x-intercepts are -3 and 7, and the y-coordinate of the vertex is 4.

The x-intercepts are -6 and 2, and the y-intercept is -9.

The vertex is (4, 0), and the y-intercept is 8.

The x-intercepts are -3 and 3, and the parabola passes through the point (2, 20).

A bus company usually transports 12 000 people per day at a ticket price of \$1. The company wants to raise the ticket price. For every \$0.10 increase in the ticket price, ,the number of riders per day is expected to decrease by 400. Calculate the ticket price that will maximize revenue.

Identify the binomial factors and their products.

Identify the binomial factors and their products.

Expand and simplify.

(x +5)(x + 4)

Expand and simplify.

(x - 2)(x - 5)

Expand and simplify.

(2x - 3)(2x + 3)

Expand and simplify.

(4x + 5)(3x - 2)

Expand and simplify.

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

Expand and simplify.

(6x -2)(5x + 7)

Expand and simplify.

\displaystyle (2x + 6)^2

Expand and simplify.

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

Expand and simplify.

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

Determine the equation of the parabola. Express your answer in standard form.

Evaluate.

\displaystyle 2^{-3}

Evaluate.

\displaystyle -5^{-1}

Evaluate.

\displaystyle (\frac{2}{5})^{-2}

Evaluate.

\displaystyle (-9)^0

Evaluate.

\displaystyle 4^{-3}

Evaluate

\displaystyle -(\frac{1}{6})^{-2}

Which is greater: (\frac{1}{4})^2 or 3^{-2}. Show your reason without using a calculator.

For what positive values of x is x^2 greater than 2^x?

How do you know?