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Problem 12Let f (x) = -2x2 + 8x - 1.Find the vertex . SHOW ALL WORK algebraically:(6) Write the function in vertex form:(c) Find the X-intercepts ALGEBRAICALLY. Giv...

Question

Problem 12Let f (x) = -2x2 + 8x - 1.Find the vertex . SHOW ALL WORK algebraically:(6) Write the function in vertex form:(c) Find the X-intercepts ALGEBRAICALLY. Give EXACT ANSWERS (no decimals). Simplify all radicals

Problem 12 Let f (x) = -2x2 + 8x - 1. Find the vertex . SHOW ALL WORK algebraically: (6) Write the function in vertex form: (c) Find the X-intercepts ALGEBRAICALLY. Give EXACT ANSWERS (no decimals). Simplify all radicals



Answers

Find the vertex and axis of the parabola, then draw the graph by hand and verify with a graphing calculator. $$f(x)=-\frac{1}{2}(x+8)^{2}+12$$

This is problem number 12 we are given the following function F of X equals negative one half times X plus a squared plus 12. Enter test with finding the vertex access and overall plot, recall that ignoring shifting the basic form of a problem is as follows, X minus H squared plus K. In this case we have H equal to negative eight and Kay equal to positive 12. Well now look at our vertex so you know that the vertex rests on the point H comma K. So this will give us the point negative eight comma 12 for our access. We know that this rests on the line X equals H. Which in this case gives us the line X equal to negative eight, plotting our parabola and gizmos. We get the following here we have our access and here we see our fair tax.

For any quartet. IQ function effects is equals. Toe X squared plus B x plus e. The word eggs exploit is given as minus with the right way to wear an F minus. Billy vibrato where the X coordinate off the verdicts is given as minus video to it and why, According it is, given it Ifo minus. We divide me too. The function be have is effects is the question x x squared plus 12 So x coordinate of the vortex will be minus be divided by two and that is nothing but minus zero divided by two multiply one that equal to zero. So why corden? It will be if off the that is equal to 12. So the vortex for the given quadratic function is zero comma.

We need to rewrite the following quadratic in vertex forms we have x squared minus 12 X Equals, we moved to 32 over. So that's -32. We take our middle term, which is negative 12 divided by two square it, So that's negative six plus -6 square. That's plus 36. So we have 36 to both sides. So this becomes the quantity X -6 squared is equal to four. We now write the function F of X is equal to the quantity X minus six squared, remove the four over minus four. So this is a vertex form.

We need to rewrite the following and standard form and give the vertex we have X squared minus 12 X. We're going to move the 32 to the other side of the equal science. It's negative 32. We take the middle term Is -12 divided by two squared. We put it here so negative 12 divided by two is 6 Square. It is plus 36. So we add 36 to both sides. We get X -6 squared is equal to four. Sorry, equation becomes affects Is equal to the quantity X -6 square. We move therefore over, she becomes -4. So this follows our standard form of F of X is equal to a times X minus H squared plus K. Our vertex comes from H K. So H Corresponds to six and K corresponds to -4.


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