Solving quadratics

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 are the types of solutions a quadratic equation can have?

Back

A quadratic equation can have one real solution, two real solutions, or two nonreal (imaginary) solutions.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, given by the coordinates (h, k) in the vertex form y = a(x - h)² + k.

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 equation x = -b/(2a) for the quadratic equation ax² + bx + c.

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the values of x that make the function equal to zero, found by solving the equation ax² + bx + c = 0.

Front

How do you find the zeros of a quadratic equation using factoring?

Back

To find the zeros using factoring, rewrite the quadratic equation in the form (x - p)(x - q) = 0, where p and q are the zeros.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Front

What does the discriminant tell you about the solutions of a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means two real solutions, D = 0 means one real solution, and D < 0 means two nonreal (imaginary) solutions.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.