In the diagram A(1;0) is the turning point of the parabola f, that intersects the y-axis at B(0;-4)

Question

1) Determine the equation of the parabola in the form f(x) = ax^2+bx+c. 2) Draw the function h(x) = 2^x+2 - 8 in the same axis as f, clearly indicating with the x-axis and y-axis. (^x+2) are both exponential to the 2. 3) Use the graph to solve for x if 2^x+2(both exponential to 2) >- 4x^2 - 8x +4

Comments

I can't see any diagram, is there any that you forgot to post?

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It won't let me post a picture or 8 just don't know how, but I replied to the email. So let me know if you get it

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You should be able to upload a photo using the picture icon in the menu bar above. You can use a screen snapshot or an actual photo in your photo folder or album. Sometimes, however, network problems prevent you from doing this (as I have experienced), but the method usually works. You are prompted for a file location when you use the upload tab in the feature, and the system will upload from the local file on your device to the MHA server’s public file in just a few seconds. You can adjust the size of the uploaded image. I usually reduce it from 600 (default) to 550 or lower. This is how I produced the picture in my solution.

If you try to use any other method the image probably won’t display to other users. If you try to provide a link to a public file, the MHA system is likely to class your submission as requiring approval, which will delay your question from being seen on the system.

Answer 1

Here are the graphs of the parabola f (red) and exponential curve h (blue).

(1) The vertex form of the parabola is (y-k)=a(x-h)², where (h,k) is the vertex or turning point given as A(1,0), so y=a(x-1)². The y-intercept at -4 is when x=0, so -4=a and the equation of the parabola is y=-4(x-1)², which expands to y=-4x²+8x-4.

(2) h(x)=2ˣ⁺²-8 is plotted in blue and shown intersecting f(x).

(3) When y=f(x)=h(x), -4x²+8x-4=2ˣ⁺²-8, 2ˣ⁺²=-4x²+8x+4. So the graph shows the intersection of the two graphs. But we need the case for h(x)>f(x), that is, 2ˣ⁺²>-4x²+8x+4, which is where the blue curve is above the red curve. From the picture, this happens when x<0 and when x>1.

I note that you have -8x instead of +8x—is this an error? If it’s not an error, the graph can’t help and the solution for x includes an irrational (x>0 and x<-2.34 approx). If it is an error, the solution is x<0 and x>1.