How do you find the important points to graph y = (x - 3)² + 1?

1 Answer
Nov 2, 2015

See explanation

Explanation:

Standard form of the equation is
y=ax^2+bx+c
Note that a could be of value 1
If a is positive then the graph is a horse shoe shape with the curve at the bottom. If negative then the other way round.

Square the bracket and then add the 1 giving:
y=x^2 - 6x +4
Tony B

Using standard form equation

x" of "(x,y)_("minimum")" is "(-1/2) times b/a

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So for your case we have:

color(green)(x" of "(x,y)_("minimum") =(-1/2) times (-6) = color(green)(+3))

color(red)("substitute "x=3" in your equation to find "y_("minimum"))

y = (3)^2 -6(3)+4
y =13 - 18
y = -5
color(green)(y" of " (x,y)_("minimum")=(-5)

Putting it all together

color(green)( (x,y)_("minimum")=(3,-5)
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color(green)("To find x-intercepts substitute y=0 and solve")

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color(green)("To find y-intercepts substitute x=0 and solve")

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