Solving Quadratics by using the Quadratic Formula

Front

What is the Quadratic Formula?

Back

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

Front

What are the coefficients in a quadratic equation?

Back

In a quadratic equation of the form ax² + bx + c = 0, 'a' is the leading coefficient, 'b' is the linear coefficient, and 'c' is the constant term.

Front

How do you identify a quadratic equation?

Back

A quadratic equation is identified by its highest degree of 2, typically in the form ax² + bx + c = 0, where a ≠ 0.

Front

What does the discriminant (b² - 4ac) tell us?

Back

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

Front

Solve using the Quadratic Formula: x² + 4x + 3 = 0

Back

x = -1 and x = -3.

Front

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

Back

The leading coefficient is 1.

Front

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

Back

x = -8 and x = 4.

Front

Determine the values of a, b, and c for the equation 4x² - 8x = 3.

Back

a = 4, b = -8, c = -3.

Front

Solve using the Quadratic Formula: x² + 12x - 5 = 0

Back

x = -6 + √41 or x = -6 - √41.

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.