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In Exercises 47-56, write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point.
Vertex: $ ( 5, 12 ) $; point: $ ( 7, 15 ) $
$y=\frac{3}{4}(x-5)^{2}+12$
Algebra
Chapter 2
Polynomial and Rational Functions
Section 1
Quadratic Functions and Models
Quadratic Functions
Complex Numbers
Polynomials
Rational Functions
Campbell University
Harvey Mudd College
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let's write the standard form of this equation that has the given vortex five twelve and passes through the point seven fifty. So my standard form, we're looking for an expression that's given on the right hand side, where the point h k is the vortex. So in our case, eight people seven Excuse me, H equals five, and Katie was twelve. That's given by this over here. So using this information, we can rewrite our earth by replacing the ancient pain. And then now we use the fact that paragraph passes through this point over here. So this means fof seven is fifteen. So let's use that fact by plugging in seven over here into the right hand side. So we have seven minus five. That's two. And then that square add in the twelve and were given that this equals fifteen. So then now we just have to solve for eight. So let's go ahead and subtract this twelve on both sides that will give you for a equals three and then this implies, eh? Three or four. And now, finally, we go back to our equation f over here, and we plug in the value of a that we just found. And we leave the agent decay as they are five and twelve. So this is the standard form of the proble, and that's our answer.
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