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

What does the 'a' value represent in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'a' represents the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What does the 'b' value represent in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'b' is the coefficient of x and affects the position of the vertex of the parabola along the x-axis.

Front

What does the 'c' value represent in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'c' is the constant term and represents the y-intercept of the parabola.

Front

How do you identify the 'c' value in the equation y = 16x² - 8x - 24?

Back

The 'c' value is -24.

Front

How do you solve a quadratic equation using the Quadratic Formula?

Back

To solve using the Quadratic Formula, identify a, b, and c from the equation, then substitute these values into x = (-b ± √(b² - 4ac)) / (2a) to find the solutions.

Front

What is the discriminant in the Quadratic Formula?

Back

The discriminant is the part of the formula under the square root, b² - 4ac. It determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

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

Back

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

Front

Solve the equation 2x² + 7x - 15 = 0.

Back

The solutions are x = -5 and x = 3/2.

Front

Use the Quadratic Formula to find the solutions for y = -x² - 5x + 12.

Back

The solutions are x = -6.77 and x = 1.77.