Which quadratic function in vertex form can be represented by the graph that has a vertex of (3, 7) and passes through the point (1, -10)? A y=−3/4(x+3)2 squared−7
y is equal to negative 3 fourths times open paren x plus 3 close paren squared minus 7

B y=−3/4(x−3)2 squared−7
y is equal to negative 3 fourths times open paren x minus 3 close paren squared minus 7

C y=3/4(x+3)2 squared+7
y is equal to 3 fourths times open paren x plus 3 close paren squared plus 7

D y=3/4(x−3)2 squared+7

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Step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4