Quadratics Flashcard Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

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

Back

The 'a' value determines the direction of the parabola's opening: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

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 formula x = -b/(2a).

Front

What are the roots of a quadratic equation?

Back

The roots (or zeros) are the x-values where the graph intersects the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of the parabola when it opens downwards.

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex of the parabola when it opens upwards.

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 equation y = ax² + bx + c.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.