How do you graph $Y = x^{2} + 5 x + 3$ $Y=x^2+5x+3$ ?

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How do you graph $Y = x^{2} + 5 x + 3$ $Y=x^2+5x+3$ ?

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Answer 1 · 2018-01-18T16:40:40

We can use a trick to create an identity which will make it easier for us to identify the function and graph it properly..

$y = x^{2} + 5 x + 3 = x^{2} + 2 \frac{5}{2} x + \frac{25}{4} - \frac{13}{4} = (x^{2} + 2 \frac{5}{2} x + \frac{25}{4}) - \frac{13}{4}$ $y=x^2+5x+3=x^2+2 5/2x+25/4-13/4=(x^2+2 5/2x+25/4)-13/4$

$= {(x + \frac{5}{2})}^{2} - \frac{13}{4}$ $=(x+5/2)^2-13/4$

${(x + \frac{5}{2})}^{2}$ $(x+5/2)^2$ is the parabola graph with vertex: minimum at $(- \frac{5}{2}, 0)$ $(-5/2,0)$ ,

enter image source here

${(x + \frac{5}{2})}^{2} - \frac{13}{4}$ $(x+5/2)^2-13/4$ is the graph of ${(x + \frac{5}{2})}^{2}$ $(x+5/2)^2$ shifted $\frac{13}{4}$ $13/4$ points downwards.

enter image source here

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How do you graph $Y = x^{2} + 5 x + 3$ $Y=x^2+5x+3$ ?

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