ACP Review Fall 24

Front

What is the absolute value function and how is it represented mathematically?

Back

The absolute value function, denoted as |x|, represents the distance of x from 0 on the number line. It is defined as: |x| = x if x >= 0, and |x| = -x if x < 0.

Front

How do you solve an equation involving absolute values, such as |a| = b?

Back

To solve |a| = b, you set up two cases: a = b and a = -b, then solve for a in both cases.

Front

What are the roots of a polynomial function?

Back

The roots of a polynomial function are the values of x for which the polynomial equals zero. They can be found by factoring, using the quadratic formula, or graphing.

Front

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, such as ax^2 + bx + c > 0. The solution set is the range of x values that satisfy the inequality.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts. Plot these points and draw a parabola opening upwards or downwards based on the leading coefficient.

Front

What is the transformation of a function?

Back

A transformation of a function involves changing its position, size, or orientation on the graph. Common transformations include translations, reflections, stretches, and compressions.

Front

What does it mean to vertically stretch a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller and narrower.

Front

What is the effect of translating a function vertically?

Back

Translating a function vertically means shifting the graph up or down by adding or subtracting a constant from the function's output.

Front

How do you solve a system of equations using matrices?

Back

To solve a system of equations using matrices, you can represent the system in matrix form (Ax = B) and use methods like Gaussian elimination or matrix inversion.

Front

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

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots of a quadratic equation: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.