Step-by-step explanation:
1. C(x) is in vertex form so let write the function out.
[tex]a(x - 1) {}^{2} + b[/tex]
B is our maximum value so b=9.
[tex]a(x - 1) { }^{2} + 9[/tex]
To find a, we know that when x=5 is a root so plug 5 in for x to find a.
[tex]a(5 - 1) {}^{2} + 9 = 0[/tex]
[tex]a(4) {}^{2} + 9 = 0[/tex]
[tex]16a = - 9[/tex]
[tex]a = - \frac{9}{16} [/tex]
2.. Let convert Chelesa function into. standard form.
[tex] \frac{ -9 }{16} (x - 1) {}^{2} + 9[/tex]
[tex] - \frac{9}{16} (x {}^{2} - 2x + 1) + 9[/tex]
[tex] - \frac{9}{16} {x}^{2} + \frac{9}{8} x + \frac{135}{16} [/tex]
Let see which value has the higher constant.
135/16 is more than 8 so Chelsea jumper higher.
3. Set Herritea equation equal to zero.
[tex] - \frac{2}{9} {x }^{2} + 8 = 0[/tex]
[tex] - \frac{2}{9} x {}^{2} = - 8[/tex]
Multiply both sides by the reciprocal of negative 2/9.
[tex] {x}^{2} = - 8 \times - \frac{9}{2} [/tex]
[tex] {x}^{2} = 36[/tex]
[tex]x = 6[/tex]
We talking positive distance so the answer is she has moved 6 units horinzontial.
4. The domain of C is all real numbers and the range is All real numbers that are less than or equal to 9.
The domain of H is all real numbers, the range of H is all real numbers that are less than or equal to 8.
5. That means that the y values are equal when x=3.7