Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Identify the 'a' value in the equation y = 16x² - 8x - 24.

Back

The 'a' value is 16.

Front

Identify the 'b' value in the equation y = 16x² - 8x - 24.

Back

The 'b' value is -8.

Front

Identify the 'c' value in the equation y = 16x² - 8x - 24.

Back

The 'c' value is -24.

Front

Solve the quadratic equation 2x² + 7x - 15 = 0 using the quadratic formula.

Back

x = -5 or x = 3/2.

Front

Solve the quadratic equation 2x² - 9x - 35 = 0 using the quadratic formula.

Back

x = -5/2 or x = 7.

Front

Solve the quadratic equation 2x² + 2x - 12 = 0 using the quadratic formula.

Back

x = 2 or x = -3.

Front

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

Back

The discriminant determines the nature of the roots: if > 0, two distinct 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.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula h = -b/(2a) and then substituting h back into the equation to find k.