Unit 3B Test Review

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola (upward or downward).

Front

How do you find the x-intercepts of a quadratic equation?

Back

To find the x-intercepts of a quadratic equation, set y = 0 and solve the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax^2 + bx + c = 0.

Front

What does it mean for a quadratic inequality to be satisfied?

Back

A quadratic inequality is satisfied when the values of x make the inequality true, meaning the corresponding y-values fall within the specified range.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the coefficient 'a' in the quadratic equation y = ax^2 + bx + c. If a > 0, the parabola opens upward; if a < 0, it opens downward.

Front

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

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

How do you solve a quadratic inequality?

Back

To solve a quadratic inequality, first solve the corresponding quadratic equation to find the critical points, then test intervals between these points to determine where the inequality holds true.

Front

What is the vertex form of a quadratic equation?

Back

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