Question

The vertex of this parabola is at (3, -2). When the x-value is 4, the y-value is 3. What is the coefficient of the squared expression in the parabola's equation?

Answer 1

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.

Answer 2

Answer:
`\left ( y+2\right )^2=25\left ( x-3\right )`

Explanation:

Given

Vertex of Parabola is
`\left ( 3,-2\right )`

and parabola passes through
`\left ( 4,3\right )`

Let us take a parabola of the form

`\left ( y-y_0\right )^2=4a\left ( x-x_0\right )`

And here
`\left ( x_0,y_0\right ) is \left ( 3,-2\right )`

therefore

`\left ( y+2\right )^2=4a\left ( x-3\right )`

Now put
`\left ( 4,3\right)` as it lies on parabola

`\left ( 3+2\right )^2=4a\left ( 4-3\right )`

`a=(25)/(4)`

Thus Equation of parabola is

`\left ( y+2\right )^2=25\left ( x-3\right )`