Algebra help needed - unsure to graph function

Question

For the function f(x)= x^2 -8x + 7

The parabola moves up, the y intercept is 7 and the vertex is (4,-9)

Graph the function clearly showing the y intercept its symmetric point and the vertex

domain: ___ Range ____

Answer 1

x^2 -8x +7

= (x-4)^2 -9 in vertex form, (x-h)^2 +k where (h,k)=vertex

= (x-7)(x-1) where 1 and 7 are the x intercepts or the points (1,0) and (7,0)

plot the points, the vertex (4,-9), the x intercepts (1,0), (7,0) the y intercept (0,7) and a symmetrical point (8,7) (image of (0,7) reflected across the axis of symmetry. Then draw a smooth parabolic curve through those 5 points.

or use a graphing calculator, Desmos, another online graphing calculator or a hand held calculator such as TI84+

domain is all real numbers

range is limited to x> -9

it's an upward opening parabola with axis of symmetry x = 4, the same as the x coordinate of the vertex which is the minimum point of the curve

y intercept is 7 which is the point (0,7) on the y axis

x intercepts are