Find the quadratic function whose graph passes through the given points. (-1,4), (0,3), (1,4).

Friday, June 5, 2015

Find the quadratic function whose graph passes through the given points. (-1,4), (0,3), (1,4).

Let us say the quadratic function is;

$\displaystyle{y}={a}{{x}}^{{2}}+{b}{x}+{c}$ where a,b and c are constants and $\displaystyle{a}\ne{0}$ .

It is given that graph passes through (-1,4).

$\displaystyle{4}={a}{{\left(-{1}\right)}}^{{2}}+{b}{\left(-{1}\right)}+{c}$

$\displaystyle{4}={a}-{b}+{c}-------{\left({1}\right)}$

Similarly by applying passing points (0,3) and (1,4) we can obtain the following equations.

$\displaystyle{3}={a}{{\left({0}\right)}}^{{2}}+{b}{\left({0}\right)}+{c}$

$\displaystyle{3}={c}------{\left({2}\right)}$

$\displaystyle{4}={a}{{\left({1}\right)}}^{{2}}+{b}{\left({1}\right)}+{c}$

$\displaystyle{4}={a}+{b}+{c}----{\left({3}\right)}$

$\displaystyle{\left({1}\right)}+{\left({3}\right)}$

$\displaystyle{8}={2}{a}+{2}{c}$

From (2) $\displaystyle{c}={3}$

$\displaystyle{8}={2}{a}+{2}\times{3}$

$\displaystyle{a}={1}$

From (3);

$\displaystyle{4}={a}+{b}+{c}$

$\displaystyle{4}={1}+{b}+{3}$

$\displaystyle{b}={0}$

So the quadratic function is $\displaystyle{y}={{x}}^{{2}}+{3}$

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