1. Answer: y = (x + 3)² - 4
<u>Step-by-step explanation:</u>
Vertex format is: y = a(x - h)² + k
y = x² + 6x + 5
y - 5 = x² + 6x <em>subtracted 5 from both sides</em>
y - 5 + = x² + 6x + <em>completed the square</em>
y + 4 = (x + 3)² <em>simplified</em>
y = (x + 3)² - 4 <em>subtracted 4 from both sides</em>
Equation is now in vertex form!
To graph the equation, plot the following points:
- vertex (h, k) = (-3, -4)
- y-intercept from the original equation (0, c) = (0, 5)
- mirror image of y-intercept (-6, 5)
2. Answer: y = -(x + 3)² + 2
<u>Step-by-step explanation:</u>
Vertex format is: y = a(x - h)² + k
y = -x² - 6x - 7
y + 7 = -x² - 6x <em>added 7 to both sides</em>
-y - 7 = x² + 6x <em>divided both sides by -1</em>
-y - 7 + = x² - 6x + <em>completed the square</em>
-y + 2 = (x + 3)² <em>simplified</em>
y - 2 = -(x + 3)² <em>divided both sides by -1</em>
y = -(x + 3)² + 2 <em>subtracted 4 from both sides</em>
Equation is now in vertex form!
To graph the equation, plot the following points:
- vertex (h, k) = (-3, 2)
- y-intercept from the original equation (0, c) = (0, -7)
- mirror image of y-intercept (-6, -7)