Solving Quadratic Equations Review

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 are the coefficients in a quadratic equation?

Back

In a quadratic equation of the form ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

How do you identify a quadratic equation?

Back

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

Front

What does the discriminant tell us?

Back

The discriminant (D) is given by b² - 4ac. It indicates the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means two complex roots.

Front

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

Back

x = -8 and x = 4.

Front

What are the factors of x² - 8x - 48?

Back

The factors are (x - 12)(x + 4).

Front

How do you convert a quadratic equation to standard form?

Back

To convert to standard form, rearrange the equation to the form ax² + bx + c = 0 by moving all terms to one side.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation 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?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h), where f(h) is the value of the function at 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 images, given by the equation x = -b/(2a).