Question

Part 1: Solve each of the quadratic equations below. Show your work. (3 points)

x2 − 25 = 0 and x2 = 2x + 15

Part 2: Describe what the solution(s) represent to the graph of each. (2 points)

Part 3: How are the graphs alike? How are they different?

Answer 1

well for the first one
x² - 25 = 0
you can add 25 to both sides
x² = 25
x = √25
\[x = \pm 5\]

for the second one

x2 = 2x + 15

get all terms on the left side...so subtract 2x and 15 from both sides

x² - 2x - 15 = 0

now...what 2 numbers multiply to -15...and also add to -2?

(x - 5)(x + 3)

lets check

x² + 3x - 5x +15
x² - 2x + 15

it checks out...so now using what we just got

(x - 5)(x + 3)

how do we get 0's from these?

? - 5 = 0?
? + 3 = 0?