Explanation
[tex]y = a {(x - h)}^{2} + k[/tex]
where a-term determines the shape of graph.
h-term determines the change of graph for x-axis.
k-term determines the change of graph for y-axis.
Vertex of the graph is at (h,k).
- Substitute the vertex value in the equation.
[tex]y = a {(x - 7)}^{2} + 2[/tex]
We need to find the value of a-term. We have the given root which we can substitute in the equation.
Also the roots are on x-axis, meaning that the y-value for roots must be 0.
- Substitute (5,0) in the equation.
[tex]0 =a {(5 - 7)}^{2} + 2 \\ 0 =a {( - 2)} ^{2} + 2 \\ 0 = 4a + 2[/tex]
[tex]4a + 2 = 0 \\ 4a = - 2 \\ a = \frac{ - 2}{4} \\ a = - \frac{1}{2} [/tex]
Therefore the value of a is - 1/2. Rewrite the equation as we get the answer.
Answer
[tex] \large \boxed{y = - \frac{1}{2} {(x - 7)}^{2} + 2}[/tex]
