Quadratics Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + 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 ax^2 + bx + c = 0, where a, b, and c are constants.

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) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What are the x-intercepts of a quadratic function?

Back

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

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

What does it mean for a quadratic function to be positive?

Back

A quadratic function is positive when its graph is above the x-axis, meaning f(x) > 0 for certain values of x.

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, given by the equation x = -b/(2a).

Front

How can you determine the direction of opening of a parabola?

Back

The direction of opening is determined by the coefficient 'a' in the quadratic function: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b^2 - 4ac, which determines the nature of the roots.