Test Review Quadratics

Front

What is a quadratic function?

Back

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

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What does it mean if h(10) = 0?

Back

It means that x = 10 is a root of the function h(x), indicating that the graph of the function intersects the x-axis at this point.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How can you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

Front

What is the formula for the vertex of a parabola in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(h) is the value of the function at x = h.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the effect of changing the value of 'a' in a quadratic function?

Back

Changing the value of 'a' affects the width and direction of the parabola: larger |a| makes it narrower, while smaller |a| makes it wider.