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# Parabola

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Find the equation whose graph is a parabola with vertex (2,4), vertical axis of symmetry, and contains the point (-1,-1). Express your answer in the form "ax^2 + bx + c".

Nov 19, 2021

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Find the equation whose graph is a parabola with vertex (2,4), vertical axis of symmetry, and contains the point (-1,-1).

Hello Guest!

$$f(x)=a (x-2)^2+4\\ a ((-1)-2)^2+4=-1\\ 9a=-5\\ \color{blue}a=-\frac{5}{9}\\ f(x)=-\frac{5}{9}(x^2-4x+4)+4$$

$$f(x)= -\dfrac{5}{9}x^2+\dfrac{20}{9}x+\dfrac{16}{9}$$

!

Nov 19, 2021
edited by asinus  Nov 19, 2021