<span>4x-y = 15
3x+2y = -8
Multiplying the first equation by two makes for an easy elimination of the y variable.
8x - 2y = 30
3x + 2y = -8
Add vertically.
11x = 22.
Divide by 11 on both sides and get x = 2.
Plug into an equation.
4(2) - y = 15
8 - y = 15
8 = 15 + y
8 - 15 = y
-7 = y.
Thus the solution is indeed (2, -7).</span>
Answer:
The answer is the first option I hope it helps
I'll do the first one to get you started
The equation y = x^2+16x+64 is the same as y = 1x^2+16x+64
Compare that to y = ax^2+bx+c and we see that
a = 1
b = 16
c = 64
Use the values of 'a' and b to get the value of h as shown below
h = -b/(2a)
h = -16/(2*1)
h = -8
This is the x coordinate of the vertex.
Plug this x value into the original equation to find the corresponding y value of the vertex.
y = x^2+16x+64
y = (-8)^2 + 16(-8) + 64
y = 0
Since the y coordinate of the vertex is 0, this means k = 0.
The vertex is (h,k) = (-8, 0)
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So we found that a = 1, h = -8 and k = 0
Therefore,
f(x) = a(x-h)^2 + k
f(x) = 1(x-(-8))^2 + 0
f(x) = (x+8)^2
is the vertex form
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<h3>Final answer to problem 1 is f(x) = (x+8)^2 </h3>
![\\ \\ ={ \left[ -\frac { { 2x }^{ 2+1 } }{ 2+1 } -\frac { 5{ x }^{ 1+1 } }{ 1+1 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%20%7B%202x%20%7D%5E%7B%202%2B1%20%7D%20%7D%7B%202%2B1%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%201%2B1%20%7D%20%7D%7B%201%2B1%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
![\\ \\ ={ \left[ -\frac { 2{ x }^{ 3 } }{ 3 } -\frac { 5{ x }^{ 2 } }{ 2 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%202%7B%20x%20%7D%5E%7B%203%20%7D%20%7D%7B%203%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%202%20%7D%20%7D%7B%202%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
