Answer:
[tex]y = {(x - 4)}^{2} - 1[/tex]
Step-by-step explanation:
[tex]y = a(x - h)^{2} + k[/tex]
We know the value of h and k.
[tex]y = a(x - 4)^{2} - 1[/tex]
The graph passes through (2,3). Therefore, substitute x = 2 and y = 3.
[tex]3 = a {(2 - 4)}^{2} - 1[/tex]
Solve for a.
[tex]3 = a {( - 2)}^{2} - 1 \\ 3 = 4a - 1 \\ 3 + 1 = 4a \\ 4 = 4a \\ \frac{4}{4} = a \\ 1 = a[/tex]
Therefore, a = 1. Rewrite the equation.
[tex]y = 1 {( x - 4)}^{2} - 1 \\ y = {(x - 4)}^{2} -1[/tex]
Answer Check
Substitute x = 2 and y = 3 in the equation.
[tex]3 = {(2 - 4)}^{2} - 1 \\ 3 = {( - 2)}^{2} - 1 \\ 3 = 4 - 1 \\ 3 = 3[/tex]
The equation is true for (2,3). Therefore, the answer is —
[tex]y = {(x - 4)}^{2} - 1[/tex]
