Intro to 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 x-intercepts of a quadratic function?

Back

The x-intercepts, also known as zeros, are the points where the graph of the quadratic function crosses the x-axis, meaning the value of y is 0.

Front

What does the 'a' in a quadratic equation represent?

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)), where f(x) is the quadratic function.

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.

Front

What does it mean for a quadratic to have a maximum value?

Back

A quadratic has a maximum value when it opens downwards (a < 0), and the vertex represents this maximum point.

Front

What does it mean for a quadratic to have a minimum value?

Back

A quadratic has a minimum value when it opens upwards (a > 0), and the vertex represents this minimum point.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.