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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you find the y-intercept of a quadratic function?

Back

To find the y-intercept, substitute x = 0 into the function and solve for y.

Front

What is the vertex of a parabola?

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 vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting this x-value back into the function to find the y-coordinate.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation f(x) = 0.

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

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

Back

If 'a' is positive, the function has a minimum value at the vertex; if 'a' is negative, it has a maximum value.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.