Question

How do you use the important points to sketch the graph of `y= x^2 - 4x`?

Answer 1

See explanation

Explanation:

`color(blue)("y intercept")`

`color(purple)(y_("intercept") " is when "x=0 => y_("intercept")=0)`

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`color(blue)("x intercept")`
`x_("intercept")" at "y=0 = x^2-4x`

Factor out `x` giving:

`color(purple)(y=0=x(x-4) =>x_("intercept")=0 and x_("intercept")=4)`

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`color(blue)("vertex")`

`x_("vertex")` is `1/2` way between x intercepts (mean value)

`color(purple)(x_("vertex") = (0+4)/2=2)`

To determine `y_("vertex")` substitute for `x`

`color(purple)(y_("vertex")=x^2-4x =(2)^2-4(2)=-4)`

`color(purple)("Vertex "->(x,y)=(2,-4)`