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Graph the given function by writing it in the standard form y=a(x-h)^2+k and then using transformations on y=x^2. Find the vertex, the axis of symmetry, and the x & y intercepts of the graph of the given function.

 

y=3x^2-30x+76

 Feb 26, 2020
 #1
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y =  3x^2  -30x  + 76)

 

Complete the square on x

 

y  = 3 ( x^2  -  10x  +  25)  +  76  -  3*25

 

y  = 3  (  x  - 5) ^2   +  76   -75

 

y  = 3(x - 5)^2  + 1

 

Here;s the graph  :   https://www.desmos.com/calculator/vamctntdeo

 

The  vertex  is   ( 5 , 1)

 

The axis of symmetry ⇒    x  = 5

 

This parabola turns upward......the  vertex lies above  the  x  axis....so  there  are  no x intercepts

 

The y  intercept  =    76 

 

 

cool cool cool

 Feb 26, 2020

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