SOLUTION: Using the graph, what are the solution(s) to the equation -x2+4x+5=0 That is x squared Does this function have a maximum or a minimum? What are the coordinates of the vertex in

Algebra ->  Human-and-algebraic-language -> SOLUTION: Using the graph, what are the solution(s) to the equation -x2+4x+5=0 That is x squared Does this function have a maximum or a minimum? What are the coordinates of the vertex in       Log On


   



Question 110904: Using the graph, what are the solution(s) to the equation -x2+4x+5=0
That is x squared
Does this function have a maximum or a minimum?
What are the coordinates of the vertex in (x, y) form?
What is the equation of the line of symmetry for this graph?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
-x%5E2+%2B+4x+%2B+5+=+0
The quadratic formula for this is
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where
a = -1
b = 4
c = 5
x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A%28-1%29%2A5+%29%29%2F%282%2A%28-1%29%29+
x+=+%28-4+%2B-+sqrt%28+4%5E2+%2B+20+%29%29%2F-2%29+
The +-sqrt(-) part is the + distance of one root from the axis of
symmetry and the - distance of the other root from the axis of symmetry.
So, the axis is -b%2F%282a%29
x+=+-4+%2F+-2+
x+=+2 answer: equation of axis of symmetry
If I plug x+=+2 into the original equation, I'll get the y-coordinate of the vertex
y+=+-x%5E2+%2B+4x+%2B+5+
y+=+-4+%2B+8+%2B+5+
y+=+9
coordinates of vertex: (2,9)
The roots are 0+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ from Axis
0%2B-+sqrt%28+16+%2B+20+%29%29%2F-2%29+
%2B+6%2F-2 and
-+6%2F-2
or -3 and %2B3 on either side of x+=+2, or
x+=+-1, x+=+5 answer: solutions to equation
Looking at the 3 points, V(2,9), (-1,0) and (5,0), The vertex is
above the solution points, so the parabola curves downward. the
vertex is a maximum answer