What is the graph of $f (x) = 2 x^{2} - 3 x + 7$ $f(x) = 2x^2 - 3x + 7$ ?

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Answer 1 · 2014-09-27T11:58:22

To graph a quadratic equation we first need to factorise it into a different form.

First we check what the discriminant is equal to
Where $f (x) = a x^{2} + b x^{2} + c$ $f(x)=ax^2+bx^2+c$
$Delta$ (Discriminant) $=b^2-4ac$

In this case $Delta$ = $3^2-4*2*7$
$Delta=-47$

Because it is less than zero it can't be factored normally
Therefore we must use the The Quadratic Formula or Completing the Square

Here I have completed the square

$f(x)=2x^2-3x+7$

Remove factor from $x^2$ term

$f(x)=2*(x^2-3/2x+7/2)$

Take $x$ term, half it and then square it

$f(x)=-3/2->-3/4->9/16$

Add and then subtract this number inside the equation

$f(x)=2*(x^2-3/2x+9/16-9/16+7/2)$

Combine the first three terms in a perfect square

$f(x)=2*((x-3/4)^2-9/16+7/2)$

Equate left over terms

$f(x)=2*((x-3/4)^2+47/16)$

Multiply coefficient back in

$f(x)=2(x-3/4)^2+47/8$

This gives a turning point of $(3/4,47/8)=(0.75,5.875)$
and a $y$ intercept of $2*(3/4)^2+47/8$
$=(0,7)$

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What is the graph of f(x) = 2x^2 - 3x + 7f(x)=2x2−3x+7f(x) = 2x^2 - 3x + 7?