Homework

Problem 1 · easy

Find the vertex of f(x) = (x - 4)^2 + 7.

Problem 2 · medium

Convert to vertex form: f(x) = x^2 - 8x + 5.

Problem 3 · easy

Solve: x^2 - 7x + 12 = 0 by factoring.

Problem 4 · easy

Solve: 2x^2 - 8 = 0.

Problem 5 · medium

Use the quadratic formula to solve x^2 + 2x - 5 = 0.

Problem 6 · easy

How many real solutions does x^2 + x + 1 = 0 have?

Problem 7 · easy

Describe the end behavior of f(x) = -3x^5 + 2x.

Problem 8 · easy

Describe the end behavior of f(x) = 4x^4 - x^2 + 1.

Problem 9 · medium

State the zeros and multiplicities of f(x) = (x + 1)^3(x - 2)^2(x).

Problem 10 · medium

For f(x) = (x + 1)^3(x - 2)^2(x), which zeros does the graph cross, and which does it bounce?

Problem 11 · medium

Is x = -1 a zero of f(x) = x^3 + 2x^2 - x - 2? Show with the Factor Theorem.

Problem 12 · medium

Divide x^3 - 6x^2 + 11x - 6 by (x - 1) using synthetic division.

Problem 13 · medium

Factor x^3 - 6x^2 + 11x - 6 completely (use result from previous problem).

Problem 14 · challenge

Find all zeros of f(x) = x^3 - 3x^2 - 4x + 12. (Hint: try x = 3.)

Problem 15 · medium

Find the vertex and state the minimum value of f(x) = 2x^2 - 4x + 5.

Problem 16 · medium

A ball is thrown upward. Its height is h(t) = -16t^2 + 48t. Find the max height.

Problem 17 · medium

Use the IVT to show there is a zero of f(x) = x^3 - 2 between x = 1 and x = 2.

Problem 18 · medium

Solve by completing the square: x^2 + 6x - 7 = 0.

Problem 19 · easy

What is the leading term of f(x) = -5x^3 + 2x^6 - x?

Problem 20 · challenge

Sketch (describe) the graph of f(x) = x^2(x - 3). Zeros, end behavior, bounce or cross.

Problem 21 · medium

Find the discriminant of 3x^2 - x + 2 and state the number of real solutions.

Problem 22 · challenge

Divide 3x^3 + 5x^2 - 2x + 1 by (x + 2) using synthetic division. What is the remainder?

Problem 23 · medium

Find the maximum value of f(x) = -x^2 + 6x - 5.

Problem 24 · challenge

A parabola has vertex (2, -3) and passes through (4, 5). Find a in f(x) = a(x-2)^2 - 3.

Problem 25 · challenge

What is the sum of the zeros of x^3 - 6x^2 + 11x - 6?