Labeling Parts of a Quadratic

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, represented as a coordinate (h, k). For example, in the quadratic function y = a(x-h)² + k, (h, k) is the vertex.

Front

How do you determine the number of x-intercepts of a quadratic function?

Back

The number of x-intercepts can be determined by calculating the discriminant (b² - 4ac) of the quadratic equation ax² + bx + c = 0. If the discriminant is positive, there are two x-intercepts; if it is zero, there is one; if negative, there are none.

Front

What does it mean if a quadratic function has a maximum value?

Back

A quadratic function has a maximum value if the parabola opens downwards (a < 0). The vertex represents the maximum point.

Front

What does it mean if a quadratic function has a minimum value?

Back

A quadratic function has a minimum value if the parabola opens upwards (a > 0). The vertex represents the minimum point.

Front

How can you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set the quadratic equation equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the standard form of a quadratic function?

Back

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

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. It can be found using the formula x = -b/(2a).

Front

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

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

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

Back

Changing the value of 'b' affects the position of the vertex and the axis of symmetry, but does not change the direction of the parabola.

Front

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

Back

Changing the value of 'c' shifts the graph of the quadratic function up or down without affecting the shape or direction of the parabola.