Solving Quadratic Equations

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 and a ≠ 0.

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.

Front

What does the discriminant (b² - 4ac) indicate?

Back

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

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

Front

What is the Zero Product Property?

Back

The Zero Product Property states that if ab = 0, then either a = 0 or b = 0.

Front

Solve for x: 2x² + 6x - 7 = 0 using the Quadratic Formula.

Back

x = (-6 ± √(6² - 4*2*(-7))) / (2*2) = (-6 ± √(36 + 56)) / 4 = (-6 ± √92) / 4 = (-6 ± 2√23) / 4 = -3/2 ± √23/2.

Front

Solve for x: f(x) = x² - 7x + 10 using any method.

Back

Factoring gives (x - 2)(x - 5) = 0, so x = 2 and x = 5.

Front

What is the vertex of a parabola given by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry for a quadratic function?

Back

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

Front

How do you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if a > 0 and downwards if a < 0.