Answer:
(-1.75, -1.125) → y = 2x² + 7x + 5
(-3, -1) → y = x² + 6x + 8
(-4, -4) → y = 2x² + 16x + 28
(2.5, 20.25) → y = -x² + 5x + 14
Step-by-step explanation:
We have to find the vertices of the parabolas given in the picture.
A). y = x² + 6x + 8
We will convert this equation into vertex form as y = (x - h)² + k
then vertex will be (h, k)
y = x² + 6x + 8
y + 1 = x² + 6x + 9
y + 1 = (x + 3)²
y = (x + 3)² - 1
y = [x - (-3)]² + (-1)
So vertex will be (-3, -1)
B). y = 2x² + 16x + 28
y = 2[x² + 8x + 14]
y = 2[x² + 8x + 16 - 2]
y = 2[(x + 4)²- 2]
y = 2[{x -(-4)}² - 2]
y = [2{x-(-4)}²] - 4
Therefore, vertex will be (-4, -4)
C). y = -x² + 5x + 14
y = -[x² - 5x - 14]
y = -[x² - 2(2.5x) - (2.5)²+ (2.5)² - 14]
y = -[(x - 2.5)² - 6.25 - 14]
y = -[(x - 2.5)² - 20.25]
Therefore, vertex will be (-2.5, - 20.25)
D). y = -x² + 7x + 7
y = -[x² - 7x - 7]
y = -[ x² - 2(3.5)x + (3.5)²- (3.5)²- 7]
y = -[(x - 3.5)²-12.25 - 7]
y = -[(x - 3.5)² - 19.5]
Therefore, vertex will be (-3.5, 19.5)
E). y = 2x² + 7x + 5
y = 2[x² + (3.5)x + 2.5]
y = 2[x²+ 2(1.75)x + (1.75)²-(1.75)² + 2.5]
y = 2[(x + 1.75)²- 3.0625 + 2.5]
y = 2[{x + 1.75)² - 0.5625]
y = 2(x + 1.75)² - 1.125
therefore, vertex will be (-1.75, 1.125)
