Answer:
The vertex is the point (4,3)
Step-by-step explanation:
we have
[tex]y=\frac{3}{4}x^{2}-6x+15[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y-15=\frac{3}{4}x^{2}-6x[/tex]
Factor the leading coefficient
[tex]y-15=\frac{3}{4}(x^{2}-8x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y-15+12=\frac{3}{4}(x^{2}-8x+16)[/tex]
[tex]y-3=\frac{3}{4}(x^{2}-8x+16)[/tex]
Rewrite as perfect squares
[tex]y-3=\frac{3}{4}(x-4)^{2}[/tex]
[tex]y=\frac{3}{4}(x-4)^{2}+3[/tex] ----> equation in vertex form
The vertex is the point (4,3)
