Question 1198841
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To represent an exponent using your keyboard, type the symbol ^


Example: 
x^2 means {{{x^2}}}



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Problem 4


y = x^2  is the parent quadratic function
y = 2x^2  vertically stretches the curve by a factor of 2
y = 2(x-5)^2  shifts the curve 5 units to the right
y = 2(x-5)^2+10  shifts the curve 10 unit up


Graph:
{{{graph(500,500,-10,10,-5,15,x^2,2x^2,2(x-5)^2,2(x-5)^2+10)}}}
x^2 in red
2x^2 in green
2(x-5)^2 in blue
2(x-5)^2+10 in purple


Here's a graph of just the parent x^2 and the final result 2(x-5)^2+10
{{{graph(500,500,-10,10,-5,15,x^2,-100,-100,2(x-5)^2+10)}}}
I recommend using either Desmos or GeoGebra as a graphing tool.
Both of which are free.


Take notice how the vertex (0,0) in the parent function has been shifted 5 units right and 10 units up to arrive at (5,10) on the final result.


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Problem 5


y = 2x^2+12x-4 is of the form y = ax^2+bx+c
where,
a = 2
b = 12
c = -4


Use the first two values to find the following
h = -b/(2a)
h = -12/(2*2)
h = -3
This is the x coordinate of the vertex (h,k)


Use that to find the y coordinate of the vertex.
y = 2x^2+12x-4
y = 2(-3)^2+12(-3)-4
y = -22
The k value is k = -22


The vertex is located at (h,k) = (-3,-22)


So,
y = a(x-h)^2 + k
y = 2(x-(-3))^2 + (-22)
y = 2(x+3)^2 - 22
represents the vertex form.


Graph:
{{{drawing(500,500,-20,20,-50,50,
graph(500,500,-20,20,-50,50,-100,2x^2+12x-4),
circle(-3,-22,0.2),
circle(-3,-22,0.25),
circle(-3,-22,0.3),
locate(-16,-36,"Vertex = (-3,-22)"),
line(-11,-35,-4,-24),
line(-4,-24,-6.3124,-25.2053),
line(-4,-24,-4.1125-0.5,-26.6052)
)}}}
As mentioned in the previous problem, use graphing software to confirm the answer.
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