Question 146011: 4) Use the graph of y=-x^(2)+4x+5 to answer the following:
(Cannot paste graph)
a) Without solving the equation, or factoring, determine the solution(s) to the equation -x^(2)+4+5=0 using only the graph.
b) Does this function have a maximum or a minimum?
c) What are the coordinates of the vertex in (x,y) form?
d) What is the equation of the line of symmetry for this graph?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! a) Without solving the equation, or factoring, determine the solution(s) to the equation -x^(2)+4+5=0 using only the graph.
There are TWO solutions:points where the graph crosses the x-axis
.
b) Does this function have a maximum or a minimum?
It is a "downward" parabola, so YES, it has a maximum. Looking at the graph, it is at the peak of the parabola
.
c) What are the coordinates of the vertex in (x,y) form?
The vertex of a parabola is the high point or low point of the graph. In your case, it is the "high point". (2,9)
.
d) What is the equation of the line of symmetry for this graph?
For a parabola, the center line that splits the parabola in half is the "line of symmetry":
x = 2
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