Alg II Unit 4 Review - Questions 12 on

Front

Write the following in vertex form (Using Completing the Square): y = x^2 + 7x + 10

Back

y = \left(x + \frac{7}{2}\right)^2 - \frac{9}{4}

Front

Use the discriminant to determine the number of solutions for the quadratic equation: -2x^2 - x - 1 = 0

Back

Discriminant = b^2 - 4ac = (-1)^2 - 4(-2)(-1) = 1 - 8 = -7 (No Solutions)

Front

Simplify: √-80

Back

4i√5

Front

Use the quadratic formula to find the solutions for: -x^2 + 2x + 2 = 0

Back

x = 1 ± √3

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (b^2 - 4ac) indicates the number of solutions: positive = 2 solutions, zero = 1 solution, negative = no solutions.

Front

How do you complete the square for the equation y = x^2 + bx + c?

Back

1. Move c to the other side. 2. Take half of b, square it, and add to both sides. 3. Factor the left side.

Front

What is the quadratic formula?

Back

The quadratic formula is x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you identify the number of solutions from the quadratic formula?

Back

By evaluating the discriminant (b^2 - 4ac): if positive, two solutions; if zero, one solution; if negative, no solutions.