Answer:
y = -2(x + 1)^2 + 8
Step-by-step explanation:
The equation of a parabola can be written in the form;
y = a(x-h)^2 + k
where a is the multiplier (h,k) is the vertex
so h = -1 and k = 8
Plug in these values
y = a(x + 1)^2 + 8
So to get the value of a, we use the point where the parabola passes through which is the point (1,0)
Simply substitute the values of x and y
0 = a(1 + 1)^2 + 8
0 = a(2)^2 + 8
-8 = 4a
a = -8/4
a = -2
So therefore the equation of the parabola is ;
y = -2(x + 1)^2 + 8
The required equation of parabola with given vertex and point of passing is [tex]y=-2(x+1)^{2}+8[/tex].
Given data:
The vertex of parabola is, (-1, 8).
The vertex is passing through (1, 0).
We know that standard equation parabola is,
[tex]y=a(x-h)^{2}+k[/tex]
Here, a is any multiplier, h and k are the vertices.
From the given problem,
h = -1
k = 8
So substituting the values as,
[tex]y=a(x-(-1))^{2}+8\\y=a(x+1)^{2}+8[/tex]..............................................(1)
To obtain the value of a, we use the point where the parabola passes through which is the point (1,0). Here, x = 1 and y =0.
So,
[tex]0=a(1+1)^{2}+8\\\\a = -2[/tex]
Substitute the value of a in equation (1) as,
[tex]y=(-2)(x+1)^{2}+8\\\\y=-2(x+1)^{2}+8[/tex]
Thus, the required equation of parabola is [tex]y=-2(x+1)^{2}+8[/tex].
learn more about the parabola here:
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