Question 280497: Q. find the missing coordinate, "x" if you know that the parabola passes through the two "mirror points" (2,-4) and (x,y)?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! You need to know what the equation is:
You then need to find the axis of symmetry.
The axis of symmetry is found by the formula x = -b/2a
The values of b and a are taken from the equation.
Standard form of a quadratic equation is ax^2 + bx + c = 0
a is the coefficient of the x^2 term.
b is the coefficient of the x term.
c is the constant term.
Once you find the axis of symmetry, then you can find the mirror image value of x.
Assume your equation is x^2 - 2x - 15.
Assume your point is (3,-12).
If that point is on the graph, then the mirror image will exist and can be found using the formula above.
Here's how:
Equation is x^2 - 2x - 15
Stand form of the equation is ax^2 + bx + c = 0
a = 1
b = -2
c = -15
formula for axis of symmetry is x = -b/2a.
Substitute in that formula to get x = -(-2)/(2*1) = 2/2 = 1.
Your point is (x,y) = (3,-12).
3 minus the axis of symmetry of 1 = 2.
Your mirror image x-value will be 2 units away from the axis of symmetry in the other direction which would make it 1 minus 2 = -1
The equation will be equal to -12 when x = 3 and when x = -1.
Replace x with 3 in the original equation to get:
x^2 - 2x - 15 = (3)^2 - 2*3 - 15 = 9 - 6 - 15 = 9 - 21 = -12.
replace x with -1 in the original equation to get:
x^2 - 2x - 15 = (-1)^2 - 2*(-1) - 15 = 1 + 2 - 15 = -12
A graph of your equation with a horizontal line at y = -12 is shown below:
You can see that y = -12 when x = -1 and when x = 3.
You need to find the axis of symmetry.
In order to do that, you need to know what the equation is.
You also need to know the formula for the axis of symmetry.
You also need to know the standard form of a quadratic equation so you can find the value of a and b.
There is another way to do it without knowing the formula for the axis of symmetry but it's just as complicated and might even be more complicated so the best way is to know what the formula is and apply it.
If your original value for (x,y) is true, then you will find the mirror image this way as long as the equation is a quadratic equation.
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