Algebra 2 - Final Review

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

To find the maximum or minimum value of a quadratic function in the form y = ax² + bx + c, use the formula x = -b/(2a) to find the x-coordinate of the vertex, then substitute this value back into the function.

Front

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

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards (minimum point); if 'a' is negative, it opens downwards (maximum point).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you solve a quadratic equation using the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). It is used to find the roots of the equation ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation, and what does it tell you?

Back

The discriminant is the value b² - 4ac. It indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

How can you determine the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic function equal to zero and solving for x, either by factoring, using the quadratic formula, or completing the square.

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

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, such as ax² + bx + c < 0 or ax² + bx + c ≥ 0.