Quadratic Functions Test

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 vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, given by the coordinates (h, k) in the vertex form f(x) = a(x - h)² + k.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form f(x) = ax² + bx + c.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

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 does it mean for a quadratic function to have no real solutions?

Back

A quadratic function has no real solutions when the discriminant (b² - 4ac) is less than zero, indicating that the parabola does not intersect the x-axis.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the 'a' coefficient in the quadratic function: if a > 0, it opens upward; if a < 0, it opens downward.

Front

What is the line of symmetry for the function y = 2x² - 4x + 1?

Back

The line of symmetry is x = -(-4)/(2*2) = 1.