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.

Front

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

Back

To find the y-intercept, set x = 0 in the function f(x) and solve for f(0).

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 f(x) = 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

How can you determine if a parabola opens up or down?

Back

If the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, the parabola opens up; if 'a' is negative, it opens down.

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, passing through the vertex.

Front

What is the formula to find the vertex of a quadratic function?

Back

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

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.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.