Unit 3: 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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

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.

Front

What does the discriminant tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots of a quadratic equation: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

Front

What is the zero product property?

Back

The zero product property states that if ab = 0, then either a = 0 or b = 0.

Front

Solve the quadratic equation: x² - 5x + 6 = 0

Back

x = 2, 3.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, found at 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 formula x = -b/(2a).

Front

How do you complete the square?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract (b/2)² to form a perfect square trinomial.