We can get the exact value of a using the vertex and one point on the parabola.
[tex]\begin{gathered} V=(2,-7) \\ P=(0,-3) \end{gathered}[/tex]
This means h = 2, k = -7, x = 0, and y = -3. We use this value in the vertex form
[tex]\begin{gathered} y=a(x-2)^2+k \\ -3=a(0-2)^2-7 \end{gathered}[/tex]
Now, we solve for a
[tex]\begin{gathered} -3=4a-7 \\ -3+7=4a \\ 4a=4 \\ a=\frac{4}{4}=1 \end{gathered}[/tex]
Therefore, a is equal to 1.
The image above shows the vertex point of the given parabola. Also shows the point we used.
