What is the vertex of y=4x^2+3x+18?

1 Answer
Apr 14, 2016

color(green)("Vertex"->(x,y)->(-3/8,279/16)

Notice the way I stick with fractions. Much more pricise than decimals.

Explanation:

There are various ways of doing this. I am going to show you one of them.

Write the equation as:

y=4(x^2+3/4x)+18

color(blue)("Determine "x_("vertex"))
Multiply the 3/4 by (-1/2)

color(blue)(x_("vertex")=(-1/2)xx3/4= -3/8)

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Not that -3/8 =0.375
My graphing package has not rounded this properly to 2 decimal places
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enter image source here

color(blue)("Determine "y_("vertex"))

Substitute of x

y_("vertex")=4(-3/8)^2+3(-3/8)+18

y_("vertex")=4(+9/64)-9/8+18

color(blue)(y_("vertex")=9/16-9/8+18 = 279/16)

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color(green)("Vertex"->(x,y)->(-3/8,279/16)