Answer:
[tex]y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
Step-by-step explanation:
An equation in the vertex form is written as
[tex]y = a (x-h) + k[/tex]
Where the point (h, k) is the vertex of the equation.
For an equation in the form [tex]ax ^ 2 + bx + c[/tex] the x coordinate of the vertex is defined as
[tex]x = -\frac{b}{2a}[/tex]
In this case we have the equation [tex]y = 9x^2 + 9x - 1[/tex].
Where
[tex]a = 9\\\\b = 9\\\\c = -1[/tex]
Then the x coordinate of the vertex is:
[tex]x = -\frac{9}{2(9)}\\\\x = -\frac{9}{18}\\\\x = -\frac{1}{2}[/tex]
The y coordinate of the vertex is replacing the value of [tex]x = -\frac{1}{2}[/tex] in the function
[tex]y = 9 (-0.5) ^ 2 + 9 (-0.5) -1\\\\y = -\frac{13}{4}[/tex]
Then the vertex is:
[tex](-\frac{1}{2}, -\frac{13}{4})[/tex]
Therefore The encuacion excrita in the form of vertice is:
[tex]y = a(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
To find the coefficient a we substitute a point that belongs to the function [tex]y = 9x^2 + 9x - 1[/tex]
The point (0, -1) belongs to the function. Thus.
[tex]-1 = a(0 + \frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
[tex]-1 = a(\frac{1}{4}) -\frac{13}{4}\\\\a = \frac{-1 +\frac{13}{4}}{\frac{1}{4}}\\\\a = 9[/tex]
Then the written function in the form of vertice is
[tex]y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
Answer:
The vertex form of a parabolic function has the general formula:
f(x) = a(x-h)^2 + k where (h,k) represent the vertex of the parabola.
Therefore, to write the given equation in vertex form, we will need to transform it to the above formula as follows:
y = 9x^2 + 9x - 1
y = 9(x^2 + x) - 1
y = 9(x^2 + x + 1/4 - 1/4)-1
y = 9((x+1/2)^2 - 1/4)-1
y = 9(x + 1/2)^2 - 9/4 - 1
y = 9(x + 1/2)^2 - 13/4 ..............> The equation in vertex form
Step-by-step explanation:
Hope this helps!!! Have a great day!!! : )
