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Find a formula for the quadratic function whose graph has a vertex at(13,6) and a y intercept of y = 19.NOTE: Enter the exact answery =

Sagot :

The general equation of a parabola with vertex (h,k) is

[tex]y=C(x-h)^2+k[/tex]

In our case, we have h = 13 and k =6. So we get the equation

[tex]y=C(x-13)^2+6[/tex]

Now, to find the value of C, we will use the given y intercept. In the previous equation we should get y=19 if we replace x = 0. So

[tex]19=C(-13)^2+6\text{ = 169C + 6}[/tex]

If we subtract 6 on both sides, we get

[tex]19\text{ - 6 = 13 = 169 C}[/tex]

If we divide both sides by 169, we get

[tex]C\text{ = }\frac{13}{169}\text{ = }\frac{1}{13}[/tex]

So the general equation of the given quadratic function is

[tex]y\text{ = }\frac{1}{13}(x-13)^2+6[/tex]

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