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The-curve-y-ax-2-bx-c-crosses-the-y-axis-at-the-point-0-3-and-has-stationary-point-at-1-2-Find-the-values-of-a-b-and-c-




Question Number 56749 by pete last updated on 22/Mar/19
The curve y=ax^2 +bx+c crosses the  y−axis at the point (0,3) and has  stationary point at (1,2). Find the  values of a,b and c.
$$\mathrm{The}\:\mathrm{curve}\:\mathrm{y}=\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}\:\mathrm{crosses}\:\mathrm{the} \\ $$$$\mathrm{y}−\mathrm{axis}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{0},\mathrm{3}\right)\:\mathrm{and}\:\mathrm{has} \\ $$$$\mathrm{stationary}\:\mathrm{point}\:\mathrm{at}\:\left(\mathrm{1},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{values}\:\mathrm{of}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}. \\ $$
Answered by ajfour last updated on 22/Mar/19
c=3  2a(1)+b=0  2=a+b+3  ⇒2a+2=a+3   ⇒  a=1  and b=−2 .    y=x^2 −2x+3 .
$$\mathrm{c}=\mathrm{3} \\ $$$$\mathrm{2a}\left(\mathrm{1}\right)+\mathrm{b}=\mathrm{0} \\ $$$$\mathrm{2}=\mathrm{a}+\mathrm{b}+\mathrm{3} \\ $$$$\Rightarrow\mathrm{2a}+\mathrm{2}=\mathrm{a}+\mathrm{3}\:\:\:\Rightarrow\:\:\mathrm{a}=\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{b}=−\mathrm{2}\:. \\ $$$$\:\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{3}\:. \\ $$

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