Question 895140
set it equal to 0 and you get:


-x^2 + 7 = 0


subtract 7 from both sides and you get:


-x^2 = -7


multiply both sides by -1 and you get:


x^2 = 7


take the square root of both sides and you get:


x = plus or minus sqrt(7)


that's your solution.


plus or minus sqrt(7) are the values of x where the graph crosses the x-axis.


the graph crosses the x-axis when the value of y is equal to 0.


the two points where the graph crosses the x-axis are (-sqrt(7),0) and (sqrt(7),0).


the axis of symmetry will be between plus sqrt(7) and -sqrt(7).


this places it at x = 0.


you can also find the axis of symmetry by using the equation of x = -b/2a.


convert the equation to standard form of ax^2 + bx + c


you already have it because the equation is y = -x^2 + 7


a is the coefficient of the x^2 term and is equal to 1.
b is  the coefficient of the x term and is equal to 0 because the x term is not there.
c is the constant term and is equal to 7.


you have:


a = 1
b = 0
c = 7


replace b with 0 and a with 7 and x = -b/2a becomes x = -0/2 which becomes x = 0.


the axis of symmetry is the vertical line at x = 0 which is the same as the y-axis.


since the quadratic equation is symmetric about the axis of symmetry, every x value that is equidistant from the axis of symmetry will have an equal y value.


we'll plot x = plus or minus {sqrt(7),2,1,0} to show you what i mean.


your equation is y = -x^2 + 7


when x = plus or minue sqrt(7), y = 0
when x = plus or minus 2, y = 3
when x = plus or minus 1, y = 6
when x = 0, y = 7


note that plus or minus sqrt(7) is equal to plus or minus 2.646 rounded to 3 decimal places.


the graph of your equation looks like this:


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