Can someone tell me how to approach this, I could care less about the answer I just want to know how to solve this without Desmos.
Thank you so much!

Answer:

the vertex is at (4, -14)

Step-by-step explanation:

Review "quadratic equations."  These have three terms, and the highest power of x is x^2.  We need to identify the coefficients of the x^2, x and x^0 terms to get info needed to identify the axis of symmetry.

Given f(x) = x^2 - 8x + 2, we see that these coefficients are 1, -8 and 2.

                                                                            b

The formula for the axis of symmetry is x  = - ------

                                                                             2a

which here is x = -(-8)/[2*1], or x = 8/2  or x = 4:  the axis of symmetry.

To find the y-coordinate of the vertex, evaluate the function at x = 4:

f(4) = 4^2 - 8(4) + 2 = 16 - 32 + 2, or f(4) = -14.

Thus, the vertex is at (4, -14).  The graph is that of a parabola that opens up, and the parabola is symmetric about the vertical line x = 4.

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On a grid, Label Hours of Exercise on x axis and Test Scores on y axis. The title of the graph is Test Scores and Exercise. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 1.1, 12 and 1, 30 and 2.1, 21 and 2.5, 42 and 3.5, 30 and 3.5, 45 and 4, 55 and 5, 45 and 5.5, 60 and 5.5, 70 and 6.5, 40 and 7, 50 and 7.5, 80 and 8, 75, and 8.5, 60 and 9, 75. The ordered pair 9, 15 is circled and labeled as T. All the other points are put in an oval and labeled as P
.
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