Answer:
y = 2 (x + seven-halves) squared minus one-fourth [y = [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex] ]
Step-by-step explanation:
We know that,
vertex form is y = a(x-h)² + k
vertex is (h, k)
Now,
Given that the equation is -
y = (x+3)² + (x+4)²
= x² + 3² + 2×3×x + x² + 4² + 2×4×x
= x² + 9 + 6x + x² + 16 + 8x
= 2x² + 14x + 25
= [tex]x^{2} + 7x + \frac{25}{2}[/tex]
= [tex]x^{2} + 7x + \frac{25}{2} + \frac{49}{4} - \frac{49}{4}[/tex]
= [tex](x + \frac{7}{2} )^{2} + \frac{25}{2} - \frac{49}{4}[/tex]
= [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex]
∴ we get
The vertex form is -
y = [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex]
So,
The correct option is - y = 2 (x + seven-halves) squared minus one-fourth (y = [tex](x + \frac{7}{2} )^{2} - \frac{1}{4}[/tex] )
