Given:
The vertex of the parabola, (h, k) = (0, -7)
The parabola passes through the point (x, y) = (2,4).
To find the parabola equation:
The general form is,
[tex]y=a(x-h)^2_{}+k[/tex]Substitute h=0, k=-7, x=2, and y=4. We get,
[tex]\begin{gathered} 4=a(2-0)^2-7 \\ 4=4a-7 \\ 4a=11 \\ a=\frac{11}{4} \end{gathered}[/tex]Substitute the values of a, h, and k in the general form.
We get,
[tex]\begin{gathered} y=\frac{11}{4}(x-0)^2_{}-7 \\ y=\frac{11}{4}x^2_{}-7 \end{gathered}[/tex]Hence, the parabola equation is,
[tex]y=\frac{11}{4}x^2_{}-7[/tex]