Solving Quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you identify the coefficients a, b, and c in the quadratic equation 4x² - 8x = 3?

Back

To identify the coefficients, rewrite the equation in standard form: 4x² - 8x - 3 = 0. Here, a = 4, b = -8, and c = -3.

Front

What is the process of factoring a quadratic equation?

Back

Factoring a quadratic equation involves expressing it as a product of two binomials, typically in the form (x - p)(x - q) = 0, where p and q are the roots.

Front

What are the roots of a quadratic equation?

Back

The roots (or zeros) of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you find the zeros of the quadratic equation x² - 4x + 4 = 0?

Back

To find the zeros, factor the equation as (x - 2)² = 0, which gives the zero x = 2.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

How can you determine the number of real roots a quadratic equation has?

Back

The number of real roots can be determined using the discriminant (b² - 4ac): if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

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

Front

How do you solve the quadratic equation a² + 2a - 24 = 0?

Back

To solve, factor the equation as (a - 4)(a + 6) = 0, giving the solutions a = -6 and a = 4.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.