Solving Quadratics by Square Roots

Front

What is a quadratic equation?

Back

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

Front

What does it mean to solve a quadratic equation by taking square roots?

Back

Solving a quadratic equation by taking square roots involves isolating the squared term and then applying the square root to both sides of the equation.

Front

What is the square root property?

Back

If x² = k, then x = ±√k.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to give the constant term and add to give the coefficient of the linear term.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as (x - p)(x - q) = 0, where p and q are the roots of the equation.

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 determine the number of real solutions of a quadratic equation?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which helps determine the nature of the roots.

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 do you solve (x - 7)² + 4 = 40?

Back

First, isolate the squared term: (x - 7)² = 36. Then take the square root: x - 7 = ±6. Thus, x = 13 or x = 1.