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 quadratic equation: y = 16x² - 8x - 24

Back

The 'a' value is 16.

Front

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

Back

The 'b' value is -8.

Front

Identify the 'c' value in the quadratic 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 solutions; if it's zero, there is one real solution; if it's negative, there are no real solutions.

Front

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

Back

x = -5/2, x = 7.

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.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).