Question 1167615: https://answers.yahoo.com/question/index?qid=20201018140421AAedVNb
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! your problem is shown below:
let y = f(x).
the function becomes y = -x^2 + 8x - 7
the standard form of a quadratic equation is y = ax^2 + bx + c
a is the coefficient of the x^2 term.
b is the coefficient of the x term.
c is the constant term.
the standard form of the equation becomes y = -x^2 + 8x - 7
the vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
a is the coefficient of the x^2 term,
(h,k) is the coordinates of the vertex.
from the standard form of the equation, you would solve for the x-coordinate of the vertex by the following equation:
x = -b/(2a)
when b = 8 and a = -1, this becomes x = -8/(-2) = 4.
the y-coordinate of the vertex is found by replacing x in the standard form of the equation by 4 and solving for y.
you get y = -4^2 + 8*4 - 7 which becomes y = -16 + 32 - 7.
solve for y to get y = 9.
the vertex from the standard form of the equation is (x,y) = (4,9).
the vertex from the vertex form of the equation is (h,k) = (4,9).
the vertex form of the equation becomes y = -1 * (x-4)^2 + 9.
both standard form of the equation and vertex form of the equation can be seen in the following graph.
since both equations are equivalent, they both draw the same graph.
when you bring the equations down 5 units, you just subtract 5 from the constant term in the standard equation and you drop 5 from the value of k in the vertex form of the equation.
you get:
y = -x^2 + 8x - 12 in the standard form.
y = -(x-4)^2 + 4 in the vertex form.
both standard form of the equation and vertex form of the equation can be seen in the following graph.
you can see from both graphs that the vertex was dropped 5 units from (4,9) to (4,4).
here's a reference you might find helpful.
https://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php
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