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

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

Back

The discriminant determines the nature of the roots: if it's positive, there are two real roots; if it's zero, there is one real root; if it's negative, there are no real roots.

Front

Solve using the Quadratic Formula: x² + 4x - 40 = -8.

Back

The solutions are x = -8 and x = 4.

Front

What is the leading coefficient in the equation x² + 5x + 7?

Back

The leading coefficient is 1.

Front

Solve using the Quadratic Formula: 2x² - 9x - 35 = 0.

Back

The solutions are x = -5/2 and x = 7.

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

What is the axis of symmetry in a quadratic equation?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror images.