Quadratic Key Features

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 upwards or downwards.

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If the coefficient of the x^2 term is negative, the function has a maximum value. If it is positive, the function has a minimum value.

Front

What are x-intercepts in a quadratic function?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, meaning the output (y-value) is zero.

Front

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

Back

You can find the x-intercepts by setting the quadratic equation equal to zero and solving for x.

Front

What does it mean if a quadratic function has no x-intercepts?

Back

It means the graph does not cross the x-axis, indicating that the quadratic has no real roots.

Front

What is the standard form of a quadratic function?

Back

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

Front

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

Back

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

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 standard form.

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

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.