Question

How do you find the important points to graph `F(x)= 2x^2 - 4x +1`?

Answer 1

See explanatioin

Explanation:

`color(green)("Standard form for a quadratic is: "ax^2 + bx +c)`

`color(green)("Convert this into " a(x^2 +b/a+c/a))`

`color(green)("In your case we factorise it into")`

`color(green)(y= 2(x^2 -2x+1/2) )`

`color(green)("It is important that there is no coefficient directly in front of the "x )`

In this case we look at what is inside the brackets to get what we want.

`x^2` is positive: that gives you an upwards horse shoe shape.
`" "` If it had been negative then the horse shoe would
`" "` have been the other way up.
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`color(blue)("The maxima/minima x value is " (-1/2) times b/c)`

So for you it will be at `color(red)( x_("minima")) =(-1/2) times (-2 )=color(red)(1)`
To find the y value at the minima substitute `(-1/2) times (-2)=(1)` for x

So
`y =2x^2 - 4x + 1`
becomes:
`color(red)(y_("minima")) =2(1)^2-4(1)+1 = color(red)( -1)`

Thus:

`color(red)((x,y)_("minima"))` `color(blue)( -> (1,-1))`
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`color(blue)("To find y intercept substitute " x = 0" and solve")`

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`color(blue)("To find x intercept substitute "y=0" and solve")`

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