Algebra 2 Unit 2 Review

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 factoring?

Back

To solve a quadratic equation by factoring, rewrite the equation in standard form, factor it into two binomials, set each binomial equal to zero, and solve for the variable.

Front

What is the vertex of a quadratic function?

Back

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

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant of a quadratic equation tell us?

Back

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

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient of x² (a) is positive and downwards if a is negative.

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 of a quadratic function occurs at the vertex, which can be found using the vertex formula or by evaluating the function at the vertex's x-coordinate.

Front

What is the significance of the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the x-values where the function intersects the x-axis, indicating the solutions to the equation when set to zero.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, and zeros, then plot these points and draw a smooth curve through them.