I need help on 1 b to d Can you show all the steps to the question Consider Cons

Question

I need help on 1 b to d
Can you show all the steps to the question

Consider Consider the fallowing quadratic function: f(r) -10z: 100a 150 a). Put this equation in standard form by completing the square. There is no credit for any other method. b). What are the coordinates of the vertex? c) What is the maximum value of the function? d). At what value of r d the maximum value accur? oes e) What are the r intercepts (if any)? f. What are the u intercepts (if any? g). What is the domain? h) What is the range? i. What is the axis of symmetry j). Sketch the graph. Be sure to label al key points and indicate the axis of symmetry.

Explanation / Answer

f(x)=-10x2+100x-150

f(x)=-10(x2-10x) +150

f(x)=-10(x2-10x+25-25)+150

f(x)=-10(x-5)2+250-150

f(x)=-10(x-5)2+100

b. This equation is of the form

y=a(x-h)2+k

where vertices is at (h,k)

Therefore vertices is (5,100)

c. The function is maximum at the vertex. And the maximum value of the given function is 100

d. The maximum value of function occurs at the x coordinate of vertex which is 5

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