Algebra 2 Fall Final Review

Front

What is the solution to the equation (x-5)(x+6)=0?

Back

The solutions are x = 5 and x = -6.

Front

What does it mean to multiply rational expressions?

Back

Multiplying rational expressions involves multiplying the numerators together and the denominators together, then simplifying if possible.

Front

Describe the transformation of the absolute value function represented by the equation y=-2|x-3|+3.

Back

The function is reflected over the x-axis, stretched by a factor of 2, shifted right by 3 units, and shifted up by 3 units.

Front

What is the definition of a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are polynomials.

Front

How do you solve the equation (x-5)(x+6)=0?

Back

Set each factor equal to zero: x-5=0 or x+6=0, giving solutions x=5 and x=-6.

Front

What is the process for dividing rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the divisor and simplify.

Front

What does it mean for a function to be reflected over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient determines the direction of the parabola's opening: if positive, it opens upwards; if negative, it opens downwards.

Front

What is the quadratic formula?

Back

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