The solution is x=6 and y=5
Formula of the parabola: (x - h)²<span> = 4p(y - k)
(h,k) is a vertex, </span>(1,-9) is a vertex.
<span>h=1, k= - 9
Substitute h and k into formula </span>(x - h)² = 4p(y - k)
(x - 1)² = 4p(y + 9)
Substitute x and y of the y-intercept
(x - 1)² = 4p(y + 9), x=0,y=-6.
(0 - 1)² = 4p(-6 + 9)
1 = 4p*3
1/3 = 4p, substitute value of 4p into (x - 1)² = 4p(y + 9).
(x - 1)² = 1/3(y + 9)
x²-2x+1=(1/3)y + 3
(1/3)y = x²-2x-2
y = 3x² - 6x -6
x-intercepts, is values of x when y=0.
3x² - 6x -6 = 0
x²-2x-2=0
We will find values of x using formula.
![x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} \\ \\ a=1, b=-2,c=-2 \\ \\x= \frac{2+/- \sqrt{(-2)^{2}-4*1*(-2)} }{2*1} \\ \\x= \frac{2+/- \sqrt{4+8} }{2} \\ \\x= \frac{2+/- \sqrt{12} }{2} = \frac{2+/- 2\sqrt{3} }{2}=1+/- \sqrt{3} \\ \\x_{1} =1- \sqrt{3} , x_{2} =1+ \sqrt{3} \\ \\x_{1} =-0.732, x_{2} =2.732](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B-b%2B%2F-%20%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%20%7D%7B2a%7D%20%0A%5C%5C%20%5C%5C%20a%3D1%2C%20b%3D-2%2Cc%3D-2%0A%5C%5C%20%5C%5Cx%3D%20%5Cfrac%7B2%2B%2F-%20%5Csqrt%7B%28-2%29%5E%7B2%7D-4%2A1%2A%28-2%29%7D%20%7D%7B2%2A1%7D%20%0A%5C%5C%20%5C%5Cx%3D%20%5Cfrac%7B2%2B%2F-%20%5Csqrt%7B4%2B8%7D%20%7D%7B2%7D%20%0A%5C%5C%20%5C%5Cx%3D%20%5Cfrac%7B2%2B%2F-%20%5Csqrt%7B12%7D%20%7D%7B2%7D%20%3D%20%5Cfrac%7B2%2B%2F-%202%5Csqrt%7B3%7D%20%7D%7B2%7D%3D1%2B%2F-%20%5Csqrt%7B3%7D%20%0A%5C%5C%20%5C%5Cx_%7B1%7D%20%3D1-%20%5Csqrt%7B3%7D%20%2C%20%20x_%7B2%7D%20%3D1%2B%20%5Csqrt%7B3%7D%20%0A%5C%5C%20%5C%5Cx_%7B1%7D%20%3D-0.732%2C%20%20x_%7B2%7D%20%3D2.732%20)
f(x) = log2 x
f(40) = log2 40
40 = 2^y
2^5 = 32 and 2^6 = 64
so f(40) lies between integers 5 and 6.