Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
given a quadratic in standard form : y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
Rearrange 2v² - 12v - 29 = 3 into standard form ( subtract 3 from both sides )
2v² - 12v - 32 = 0 ← in standard form
with a = 2, b = - 12, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{-12}{4}[/tex] = 3
substitute x = 3 into the equation for corresponding value of y
y = 2(3)² - 12(3) - 32 = 18 - 36 - 32 = - 50
vertex = (3, - 50)
y = 2(v- 3)² - 50 ← in vertex form
Answer:
The vertex form is [tex]2(v-3)^{2}-50[/tex]
The vertex is (3 , -50)
Step-by-step explanation:
∵ [tex]2v^{2}-12v-29 = 3[/tex] ⇒ [tex]2v^{2}-12v-29-3=2v^{2}-12v-32=a(v+b)^{2}+c[/tex], where a , b and c are constant
[tex]2v^{2}-12v-32=a(v^{2}+2bv+b^{2})+c[/tex]
[tex]2v^{2}-12v-32=av^{2}+2abv+ab^{2}+c[/tex]⇒ compare the two sides
a = 2
2ab = -12 ⇒ 2(2)b = -12 ⇒ 4b = -12 ⇒ b = -3
[tex]ab^{2}+c=-32[/tex] ⇒ [tex]2(-3)^{2}+c=-32[/tex]
2 × 9 + c = -32 ⇒ c = -32 -18 = -50
∴ The vertex form is [tex]2(v-3)^{2}-50[/tex]
∴ The vertex is (3 , -50)
