Factor and Solve Quadratics

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 is the Zero-Product Property?

Back

The Zero-Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, you need to express it in the form (x - p)(x - q) = 0, where p and q are the roots of the equation.

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Set the equation to zero. 2. Factor the quadratic expression. 3. Apply the Zero-Product Property. 4. Solve for x.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions of the equation x² - 9x + 20 = 0?

Back

The solutions are x = 4 and x = 5.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean to solve a quadratic equation?

Back

To solve a quadratic equation means to find the values of x that make the equation true, typically the points where the graph intersects the x-axis.

Front

What is the significance of the coefficients in a quadratic equation?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.

Tags

CCSS.HSF-IF.C.7A

Front

How can you check if your solutions to a quadratic equation are correct?

Back

You can check your solutions by substituting them back into the original equation to see if they satisfy it.

Tags

CCSS.HSA-REI.B.4B

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

The sum of the roots (p + q) is equal to -b/a, and the product of the roots (p * q) is equal to c/a.

Tags

CCSS.HSF.IF.A.1

Front

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

Back

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