Fall 24 Algebraic Reasoning Final Exam Review Part 3

Front

What is the vertex of the quadratic function y = x² - 8x + 14?

Back

The vertex is (4, -2).

Front

Identify the function represented by the graph that shows exponential decay.

Back

f(x) = 2(0.75)ⁿ.

Front

Calculate the product of (5x + 2) and (x² - 3x + 6).

Back

The product is 5x³ - 13x² + 24x + 12.

Front

Simplify the expression √10 ⋅ √45.

Back

The simplified form is 15√2.

Front

Use the quadratic formula to find the solutions of 2x² - 9x - 35 = 0.

Back

The solutions are x = -5/2 and x = 7.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

Front

What does it mean for a function to be exponential decay?

Back

An exponential decay function decreases as x increases, typically in the form f(x) = a(b)ⁿ where 0 < b < 1.

Front

What is the product of two square roots, √a and √b?

Back

The product is √(a*b).

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0.