xx intercepts
To find the xx intercepts there are 3 methods. These methods are factorisation, quadratic formula, and completing the square. Factorising is the easiest method but does not work all the time, however it does in your case.
To factorise the expression we must create two brackets: (x+-f)(x+-g)(x±f)(x±g) We can figure out the values of a and b from the equation above.
The general form of a quadratic equation is ax^2 + bx + cax2+bx+c. The values of ff and gg must multiply to make cc which in your case is 4. The values must also and add together to make bb which in your case is -4. This example is easy, as both aa and bb are -2 and this satisfys both conditions above. So our factorised equation is (x-2)(x-2)(x−2)(x−2)
The solutions to the equation are the opposite value to those in the brackets. In this case this means the solutions are both just 2, and there is only one solution so there is only one point where it crosses the xx axis. Note that in examples where the brackets have a different value in them then there will be 2 points where the line crosses the xx axis.
To find the yy coordinate of this point we substitute our value of xx, 2 into the original equation.
y = (2)^2 - 4(2) + 4y=(2)2−4(2)+4
y = 4 - 8 + 4y=4−8+4
y = 0y=0
So the value of yy is 0 at this point, and our xx intercept coordinate is (2,0)(2,0). If you got two values for xx in the previous part you would have to do this twice to get both coordinates.
yy intercept
The yy intercept is much easier to find. As we know on the yy intercept the value of xx is equal to 0. Therefore we just substitute this into the equation to find the value for yy.
y = (0)^2 - 4(0) + 4y=(0)2−4(0)+4
Removing everything multiplied by 0 we get: y = 4y=4
So therefore the yy intercept coordinate is (0,4)(0,4).
