Respuesta :
the equation of a parabola in its vertex form is y=a(x-h)²+k, where (h, k) is the vertex of the parabola.
in this case, h=3, k=-2, so y=a(x-3)-2
plug (4,3) in the equation: 3=a(4-3)²-2, a=5
so the coefficient of the squared expression is 5.
in this case, h=3, k=-2, so y=a(x-3)-2
plug (4,3) in the equation: 3=a(4-3)²-2, a=5
so the coefficient of the squared expression is 5.
Answer:[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]
Step-by-step explanation:
Given
Vertex of Parabola is [tex]\left ( 3,-2\right )[/tex]
and parabola passes through [tex]\left ( 4,3\right )[/tex]
Let us take a parabola of the form
[tex]\left ( y-y_0\right )^2=4a\left ( x-x_0\right )[/tex]
And here [tex]\left ( x_0,y_0\right ) is \left ( 3,-2\right )[/tex]
therefore
[tex]\left ( y+2\right )^2=4a\left ( x-3\right )[/tex]
Now put [tex]\left ( 4,3\right)[/tex] as it lies on parabola
[tex]\left ( 3+2\right )^2=4a\left ( 4-3\right )[/tex]
[tex]a=\frac{25}{4}[/tex]
Thus Equation of parabola is
[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]
