The vertex of the parabola is at (-3,-2).
Parabola:
'A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point and from a fixed straight line.'
Vertex of a parabola:
'The vertex of a parabola is the point where the parabola crosses its axis of symmetry.'
According to the problem,
2x² + 12x + 16 is the given function f(x)
Using the form ax² + bx + c to find the values of a, b and c
⇒ a = 2, b = 12, c = 16
Using the vertex form of parabola:
a( x + d )² + e
Substituting the values of a and b in formula d = [tex]\frac{b}{2a}[/tex]
⇒ d = [tex]\frac{12}{2(2)}[/tex]
⇒ d = 3
We can find the value of e from the formula:
[tex]e = c - \frac{b^{2} }{4a}[/tex]
⇒ [tex]e =[/tex] [tex]16 - \frac{12^{2} }{4(2)}[/tex]
⇒ e = -2
Substituting values of a, d and e into the vertex form a(x + d)² + e
2(x+3)² - 2
Setting y = 2(x+3)² - 2
Using vertex form, y = a(x - h)² + k to determine the values of a, h and k
a = 2
h = -3
k = -2
Since the value of a is positive, the parabola opens up
Vertex = (h , k)
= (-3 , -2)
A second point on the parabola would be (-4 , 0) as marked on the graph.
Hence, we can conclude that the vertex of the parabola of the given function f(x) is at (-3 , -2) and the parabola opens up.
Learn more about parabola here:
https://brainly.in/question/41921538
#SPJ2
