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.

Tags

CCSS.HSA-REI.B.4B

Front

What is the square root property?

Back

If x² = k, then x = ±√k.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B