I would recommend combing like terms (ex- 10x-9x=x) so it could be 15x^2+x-6 . I recommend using something like mathpapa to show you step-by-step how to do it, and if you know, then it just gives you a quick answer
The answer is no solutions
![f(x)=\frac{x}{2}+8](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bx%7D%7B2%7D%2B8)
Given y = f(x)
Substitute x = 10.
![f(10)=\frac{10}{2} +8\\f(10)=5+8\\f(10)=13](https://tex.z-dn.net/?f=f%2810%29%3D%5Cfrac%7B10%7D%7B2%7D%20%2B8%5C%5Cf%2810%29%3D5%2B8%5C%5Cf%2810%29%3D13)
Therefore f(x) = 13 when x = 10
Answer:
A) (-8, -16)
B) (0, 48)
C) (-4, 0), (-12, 0)
Step-by-step explanation:
A) the vertex is the minimum y value.
extremes of a function we get by using the first derivation and solving it for y' = 0.
y = x² + 16x + 48
y' = 2x + 16 = 0
2x = -16
x = -8
so, the vertex is at x=-8.
the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16
B) is totally simple. it is f(0) or x=0. so, y is 48.
C) is the solution of the equation for y = 0.
the solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac)) / (2a)
in our case here
a=1
b=16
c=48
x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =
= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)
x1 = -8 + 4 = -4
x2 = -8 - 4 = -12
so the x- intercepts are (-4, 0), (-12, 0)