Ch 4 Extra Practice

Front

What are the x-intercepts of a function?

Back

The x-intercepts of a function are the points where the graph of the function crosses the x-axis, which occur when y=0.

Front

How do you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined using the discriminant (b² - 4ac) from the quadratic formula. If the discriminant is positive, there are two solutions; if it is zero, there is one solution; if negative, there are no solutions.

Front

Solve for k: k² - 6 = -50

Back

k = ±2i√11

Front

Solve for x: 2x² - 8 = 100

Back

x = ±3√6

Front

What does it mean if a quadratic equation has no solutions?

Back

It means that the graph of the equation does not intersect the x-axis, indicating that the discriminant is negative.

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 ax² + bx + c = 0.

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as √(-1).

Front

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

Back

The discriminant indicates the nature of the roots of the quadratic equation: positive for two distinct real roots, zero for one real root, and negative for two complex roots.

Front

How do you solve a quadratic equation by taking square roots?

Back

To solve by taking square roots, isolate the x² term, then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

What is the vertex of a parabola?

Back

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