Algebra, need help! Thank you.

Question

1. Write the function f(x) = 2x² - 2x - 12 in vertex form to highlight the vertex. Enter the function in vertex form and the coordinates of the vertex.

2. Write the function f(x) = 2x² - 2x - 12 in factored form to highlight the x-intercepts. Enter the function in factored form and the coordinates of the x-intercepts.



3. Sketch a graph the function f(x) = 2x² - 2x - 12. Using a paint program or on paper, make sure you label the vertex and the x-intercepts on your graph.

4. Enter the range of the graphed function using proper notation.

Answer 1

f(x) = 2(x² - x + (-1/2)²) - 12 - 1/2

f(x) = 2(x + 0.5)² - 12.5 Vertex Form

f(x) = 2x² - 2x - 12

f(x) = 2(x² - x - 6)

f(x) = 2(x - 3)(x + 2) Factored Form

From these can you sketch the graph and answer?

Answer 2

1. Write the function f(x) = 2x² - 2x - 12 in vertex form to highlight the vertex. Enter the function in vertex form and the coordinates of the vertex.

SOLUTION

f(x) = 2(x² - x) - 12 Factor the 2 out of the first two terms

= 2(x² - x + 1/4) + 1/2 -12 Complete the square on the inside of the (), (-1/2)²=1/4

=2(x - 1/2)^2 - 23/2 Factor

Vertex (1/2, -23/2)

2. Write the function f(x) = 2x² - 2x - 12 in factored form to highlight the x-intercepts. Enter the function in factored form and the coordinates of the x-intercepts.

SOLUTION

f(x) = 2(x² - x - 6) Factor the 2 out of all the terms

=2(x - 6)(x + 1) Factor the Quadratic

The x-intercepts are x = 6, -1

3. Sketch a graph the function f(x) = 2x² - 2x - 12. Using a paint program or on paper, make sure you label the vertex and the x-intercepts on your graph.

SOLUTION

I skipped this because I can't draw on here. ;)

4. Enter the range of the graphed function using proper notation

SOLUTION

The range of the function is [-23/2, ∞).