Respuesta :
The equation of parabola in vertex form is [tex]y=\frac{-3}{4}(x-3)^{2}-5[/tex]
Solution:
Given that parabola with vertex (3, -5) and going through point (1, -8)
To find : equation of parabola
The equation of parabola in vertex form is given as:
[tex]y=a(x-h)^{2}+k[/tex] ----- eqn 1
where (h, k) are the coordinates of the vertex
here (h, k) = (3, −5)
Substituting the values in above formula, we get
[tex]y=a(x-3)^{2}+(-5)[/tex]
[tex]y=a(x-3)^{2}-5[/tex] ----- eqn 2
The given equation of parabola passes through (1, -8)
Substituiting (x, y) = (1, -8) in eqn 2 we get,
[tex]\begin{array}{l}{-8=a(1-3)^{2}-5} \\\\ {-8=a(-2)^{2}-5} \\\\ {-8=a \times 4-5} \\\\ {-8+5=4 a} \\\\ {-3=4 a} \\\\ {a=\frac{-3}{4}}\end{array}[/tex]
Now substitute the value of "a" in eqn 2,
[tex]y=\left(\frac{-3}{4}\right)(x-3)^{2}-5[/tex]
Thus the equation of parabola in vertex form is found
