The equation of the parabola is:
[tex]y = \frac{3}{2}(x - 9)^2 + 1[/tex]
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The equation of a parabola with vertex (h,k) is given by:
[tex]y = a(x - h)^2 + k^2[/tex]
Vertex of (9,-1), thus [tex]h = 9, k = -1[/tex]. Then
[tex]y = a(x - 9)^2 + (-1)^2[/tex]
[tex]y = a(x - 9)^2 + 1[/tex]
Passes through (7,7), which means that when [tex]x = 7, y = 7[/tex], and this is used to find a.
[tex]y = a(x - 9)^2 + 1[/tex]
[tex]7 = a(7 - 9)^2 + 1[/tex]
[tex]7 = 4a + 1[/tex]
[tex]4a = 6[/tex]
[tex]a = \frac{6}{4}[/tex]
[tex]a = \frac{3}{2}[/tex]
Thus, the equation is:
[tex]y = \frac{3}{2}(x - 9)^2 + 1[/tex]
A similar problem is given at https://brainly.com/question/13773803
