Homework graph quadratic functions in standard form

Question

Then graph the function by hand. Y=x^2-6x+8

Please if someone can help

Answer 1

y= x^2 -6x + 8 = x^2 -6x + 9 +8-9 = 0

= x^2 -6x + 9 - 1 = 0

= (x-3)^2 -1 =0

= (x-3)^2 -1

y intercept is + 8 y coordinate of vertex =-1

vertex is (3, -1)

f(x) = (x-3)^2 -1 is the quadratic in vertex form

It's a downward opening parabola with maximum = vertex, or y=-1

take the derivative of the original equation and set it = 0

f'(x) = 2x -6 = 0

2x =6

x =3 is the x coordinate where y = max

(3)^2 - 6(3) + 8 = 9-18+8 = -1 = maximum y value

Answer 2

Answer 3

To graph in standard form ( y = a( x - h )² + k), you will need to complete the square for this function. That will tell you the vertex (h,k), the y - intercept, and if the graph opens up or down.

Another way of doing this is to first, reference the parent function for the graph f(x) = x². That will give you the general shape of this graph.

Then, find the x intercepts by setting the function equal to zero and solving for x. f(x) = 0 = x² - 6x + 8 (use any method you like to do this, I suggest using the quadratic equation method.

Next find your vertex (h,k) using the vertex equation h = -b/(2a). Note: f(x) = ax² + bx + c. Once you find "h", plug it into the function to find k.

Now you have three points you can plot, and you know the general shape of the function to sketch the graph.