9.1 Characteristics of Quadratics

Front

What are the x-intercepts of a quadratic function?

Back

The points where the graph intersects the x-axis, found by setting y = 0.

Front

What is the axis of symmetry in a quadratic graph?

Back

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

Front

Define the y-intercept of a quadratic function.

Back

The point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

What is the vertex of a parabola?

Back

The highest or lowest point on the graph of a quadratic function, depending on its orientation.

Front

What does the term 'parabola' refer to?

Back

A U-shaped graph that represents a quadratic function.

Front

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

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the significance of the leading coefficient in a quadratic function?

Back

It determines the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.

Front

What is the formula for a quadratic function in standard form?

Back

f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What are the roots of a quadratic equation?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The expression b^2 - 4ac, which determines the nature of the roots.