Solve Quadratic Equations by Factoring & Graphing

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation involves rewriting it as a product of two binomials, allowing for easier solutions.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, also known as solutions or x-intercepts.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set the quadratic equation equal to zero and solve for x.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on its orientation (upward or downward).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots.

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation, add the square of half the coefficient of x to both sides, and factor the left side.

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.