Practice Test Quadratic Functions

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac, which determines the nature of the roots of the quadratic equation ax² + bx + c = 0.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

How do you factor the expression 6m² + 16m?

Back

The expression can be factored as 2m(3m + 8).

Front

What is the vertex form of a quadratic function?

Back

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

Front

What transformation occurs when the equation f(x) = x² is changed to g(x) = (x + 4)²?

Back

This represents a horizontal translation of the graph 4 units to the left.

Front

What is the effect of the coefficient 'a' in the quadratic function y = ax²?

Back

The coefficient 'a' determines the direction and width of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens 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

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, which can be found using the vertex form or by calculating f(-b/(2a)).