How do I find any x and y intercepts of f(x) = 2x^2 - 4x + 5?
I can't figure out the actual equation for each. If someone could do it in detail for me I would really appreciate it.
I have tried and got (0,5) but not sure if this is correct either.
X and Y intercepts of a line or graph or curve means, where the line or curve or graph cuts or intersects (or touches in extreme case) X axis or Y axis. The number of intercepting points may be one or more or there may not be any intersections(or intercepts) or touching.
If x and y are related by an equation,y=f(x), then the x interecept is got by putting y=0 and solving for x value. And the y intercept is got by putting x=0 and solving for y value.
Finding x intercept:
Put y=0 in y=2x^2-4x+5 and solve for x.
2x^2-4x+5=y. The same equation reversed for my convenience please.
2x^2-4x+5= 0, as y needs to be put to 0
2(x^2-2x)+5=0, rearranged .
2[(x-1)^2 -1}+5=0, rearranged.
x-1= + or - sqrt(-3/2)
Both x values are imaginary. So no real X intercepts.
So the given curve do not cut X axis , as the zeros of the expression, 2x^2-4x+5 are imaginary.
Finding Y intercetpt:
The given curve cuts (or intercepts) axis at y = 5.
Point to ponder for you:
Your answer (0,5) is the coordinates of the point, where 2x^2-4x+5 cuts Y axis. The Y cordintate alone 5 where the curve cuts the Y axis is the Y intercept. You are very very nearly correct.
Where is the equation?
f(x) = 2x^2-4x+5 is the equatuation, or
y=2x^2-4x+5 is the equation.
Here x is the variable and for any value of x , you can find the corresponding value of 2x^2-4x+5 and that is the value of y or f(x).
Example : for x=1, 2x^2-4x+5=2*1^2-4*1+5=2-4+5=3.
So y=3, when x=1.
Hope this helps.