Solving Quadratics Review

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you complete the square for the equation x² + 6x - 4 = 36?

Back

To complete the square, rearrange the equation to x² + 6x = 40, then add (6/2)² = 9 to both sides to get (x + 3)² = 49.

Front

What are the roots of the equation x² + 6x - 4 = 36 after completing the square?

Back

The roots are x = 4 and x = -10.

Front

What is the first step in using the quadratic formula?

Back

Identify the coefficients a, b, and c from the quadratic equation in standard form.

Front

How do you solve the equation 2x² + 2x - 12 using the quadratic formula?

Back

Identify a = 2, b = 2, c = -12, then apply the quadratic formula to find the roots x = 2 and x = -3.

Front

What is the relationship between the roots of the equation 9k² = 225?

Back

The roots are k = -5 and k = 5, found by dividing both sides by 9 and taking the square root.

Front

What is the process to solve k² - 6 = 43 by taking square roots?

Back

Rearrange to k² = 49, then take the square root to find k = 7 and k = -7.

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the vertex form of a quadratic equation?

Back

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