Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written 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 function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

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 = h, where (h, k) is the vertex.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula h = -b/(2a) and then substituting h back into the function to find k.

Front

What are the roots of a quadratic function?

Back

The roots (or zeros) of a quadratic function are the values of x for which f(x) = 0, representing the x-intercepts of the graph.

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

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the function.

Front

How can you determine if a quadratic function opens upward or downward?

Back

If the 'a' value in the quadratic function is positive, the parabola opens upward; if 'a' is negative, it opens downward.