Exploring Quadratics

Answer explanation

To factor the expression x^2 + 5x + 6, we look for two numbers that multiply to 6 and add to 5. The numbers 2 and 3 fit this, so we can write it as (x + 2)(x + 3). Thus, the correct answer is (x + 2)(x + 3).

Desean begins to use the quadratic formula to solve the following equation.
Which expression shows a step in solving the above equation?

Answer explanation

To solve the equation x^2 - 3x - 9 = 0 using the quadratic formula, we rearrange it to standard form. The correct expression for the quadratic formula step is \frac{3\pm\sqrt{45}}{2}, which corresponds to the coefficients from the equation.

What are the solutions to the following quadratic?

Answer explanation

To solve the quadratic equation 7x^2 + x - 4 = 0, we can use the quadratic formula. The correct solutions are x = -0.831 and x = 0.688, which can be verified by substituting back into the original equation.

• No x-intercepts

A quadratic has a vertex at (1,2) and opens downward. For what values of x does the function increase?

• (1,infinity)

• (-infinity,1)

• (2, infinity)

• and beyond

If you have 40 feet of fencing, which function gives the area of the rectangle in terms of width (x) in STANDARD FORM?

• f(x)=x(20-x)

• f(x)=2x(20-x)

• f(x)= -x^2 + 20x

• f(x) = -2x^2+40x