Evaluating Functions

Front

What is the general form of a quadratic function?

Back

A quadratic function is generally expressed as f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function and simplify.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form f(x) = ax² + bx + c is given by the point (-b/(2a), f(-b/(2a))).

Front

What does the term 'parabola' refer to in relation to quadratic functions?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that opens upwards if a > 0 and downwards if a < 0.

Front

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

Back

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the parabola.

Front

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

Back

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

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

How do you determine if a quadratic function has real roots?

Back

A quadratic function has real roots if the discriminant (b² - 4ac) is greater than or equal to zero.

Front

What is a linear function?

Back

A linear function is a function of the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a linear function?

Back

The slope of a linear function is found by taking the difference in y-values divided by the difference in x-values between two points on the line.