Homework SourseWrite the quadratic function in standard form fx x2 14x 4
Write the quadratic function in standard form.
f(x) = x2 + 14x + 46
f(x) =
Sketch its graph.
Identify the vertex, axis of symmetry, and x-intercept(s). (If an answer does not exist, enter DNE.)
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Solution
f(x) =x2+14x +46
f(x) =x2+14x +49 -49+46
f(x) = (x+7)2-3
And that\'s the standard form
Which is in the form of
y=a(x-h)2+k
Where vertex (h,k) =(-7,-3)
TO find the x intercept, we have to plug f(x) =0
(x+7)2-3=0
(x+7)2=3
x+7=+-sqrt3
x=-7-sqrt3 , (-7-sqrt3,0) (smaller value)
x=-7+sqrt3 , (-7 +sqrt3,0) (larger value )
Symmetry
x+7=0
x=-7
Correct graph is the last one .
