1. Answer: y = (x + 3)² - 4
Step-by-step explanation:
Vertex format is: y = a(x - h)² + k
y = x² + 6x + 5
y - 5 = x² + 6x subtracted 5 from both sides
y - 5 + [tex]\bigg(\dfrac{6}{2}\bigg)^2[/tex] = x² + 6x + [tex]\bigg(\dfrac{6}{2}\bigg)^2[/tex] completed the square
y + 4 = (x + 3)² simplified
y = (x + 3)² - 4 subtracted 4 from both sides
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
Step-by-step explanation:
Vertex format is: y = a(x - h)² + k
y = -x² - 6x - 7
y + 7 = -x² - 6x added 7 to both sides
-y - 7 = x² + 6x divided both sides by -1
-y - 7 + [tex]\bigg(\dfrac{6}{2}\bigg)^2[/tex] = x² - 6x + [tex]\bigg(\dfrac{6}{2}\bigg)^2[/tex] completed the square
-y + 2 = (x + 3)² simplified
y - 2 = -(x + 3)² divided both sides by -1
y = -(x + 3)² + 2 subtracted 4 from both sides
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)
