# Pre-Calc

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for the conic y=5x^2-40x+78 find an equation in standard form and its vertex, focus, and directrix

• Pre-Calc -

complete the square
y = 5(x^2 - 8x + ....) + 78
= 5(x^2 - 8x + 16 - 16) + 78
= 5( (x-4)^2 - 16) + 78
= 5(x-4)^2 - 80 + 78
= 5(x-4)^2 - 2

take over ....

• Pre-Calc -

What's my next step??

• Pre-Calc -

We could write our answer in the form
y+2 = 5(x-4)^2

take a look at
http://jwilson.coe.uga.edu/emt725/class/sarfaty/emt669/instructionalunit/parabolas/parabolas.html
half-way down the page at example 3

• Pre-Calc -

thank you!

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