Question

How do you use the important points to sketch the graph of `f(x) = (x - 7)^2`?

Answer 1

See explanantion

Explanation:

The given equation is in vertex form: `y=a(x+b/(2a))^2 +k`

Where `(-1)xx b/(2a) = x_("vertex")` and `y_("vertex")=k`
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`y=(x-7)^2+0`

`color(blue)(=> "Vertex" -> (x,y)->(7,0))`
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Expanding the brackets gives

`y=x^2-14x+49`

`color(blue)(y_("intercept")=49)`
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`color(blue)("As the coefficient of "x^2" is +1 the graph is of general shape "uu)`
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`color(brown)("As the y part of the vertex is 0 it means that the x-axis is tangential")` `color(brown)("to the curve. In other words, the curve does not cross the x-axis.")`

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Just out of interest take another look at: `y=x^2-14x+49`

Notice that `->x_("vertex")=(-1/2)xx(-14)=+7`