SOLUTION: Give the equation of the function whose graph is describe. The graph of y=x^2 is shifted 4 units to the right. this graph is then vertically stretched by a factor of 5 and refle

Algebra ->  Graphs -> SOLUTION: Give the equation of the function whose graph is describe. The graph of y=x^2 is shifted 4 units to the right. this graph is then vertically stretched by a factor of 5 and refle      Log On


   

Question 47648: Give the equation of the function whose graph is describe.
The graph of y=x^2 is shifted 4 units to the right. this graph is then vertically stretched by a factor of 5 and reflected across the x-axis.Finally the graph is shifted 8 units upward.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
start with y+=+x%5E2
+graph%28+200%2C+300%2C+-5%2C+5%2C+-4%2C+20%2C+x%5E2%29+
Shift 4 units to the right
y+=+%28x-4%29%5E2
+graph%28+200%2C+300%2C+-2%2C+10%2C+-4%2C+20%2C+%28x-4%29%5E2%29+
Stretch in the vertical direction by factor of 5
y+=+5%2A%28x-4%29%5E2
+graph%28+200%2C+300%2C+-2%2C+10%2C+-4%2C+20%2C+5%2A%28x-4%29%5E2%29+
Reflect about the x-axis
y+=+-5%2A%28x-4%29%5E2
+graph%28+200%2C+300%2C+-2%2C+10%2C+-20%2C+4%2C+-5%2A%28x-4%29%5E2%29+
Shift 8 units upward
y+-+8+=+-5%2A%28x-4%29%5E2
+graph%28+200%2C+300%2C+-2%2C+10%2C+-10%2C+20%2C+8-5%2A%28x-4%29%5E2%29+
Solving for y,
y+-+8+=+-5%2A%28x%5E2+-8x+%2B+16%29
y+=+-5%2A%28x%5E2+-8x+%2B16%29+%2B+8
y+=+-5%2Ax%5E2+%2B+40x+-+80+%2B+8
y+=+-5%2Ax%5E2+%2B+40x+-72
Check some values to see if they make sense
When x = 4,
y+=+-80+%2B+160+-72
y+=+%2B+8
OK
Find roots (solve for y=0) use x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0
a = -5
b = 40
c = -72
x+=+%28-40+%2B-+sqrt%28+40%5E2-4%2A%28-5%29%2A%28-72%29+%29%29%2F%282%2A%28-5%29%29+
x+=+%28-40+%2B-+sqrt%281600+-+1440%29%29+%2F+-10
x+=+4+%2B-+sqrt%28160%29+%2F+-10
x+=+4+%2B-+4%2Asqrt%2810%29+%2F+10
x+=+4+%2B+1.265
x+=+4+-+1.265
These values make sense according to graph