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.

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.

Front

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

Back

The solutions are x = 4 and x = 5.

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.

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.

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.

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.