"How do you graph y=x2+7x−1?" was answered by students like you

High School
Algebra
Algebra I
Quadratic function and equation

Babenzgs

Answered question

2022-01-20

How do you graph

y = x^{2} + 7 x - 1

Answer & Explanation

Darrell Boone

Beginner2022-01-21Added 9 answers

Step 1
Given equation: $y = x^{2} + 7 x - 1$
$y = x^{2} + 2 \times \frac{7}{2} \times x + {(\frac{7}{2})}^{2} - {(\frac{7}{2})}^{2} - 1$
$y = {(x + \frac{7}{2})}^{2} - \frac{51}{2}$
${(x + \frac{7}{2})}^{2} = y + \frac{51}{2}$
${(x + \frac{7}{2})}^{2} = 4 \times \frac{1}{3} (y + \frac{51}{2})$
comparing the above equation with
${(x - x_{1})}^{2} = 4 a (y - y_{1})$
we get
$x_{1} = - \frac{7}{2}$ ,
$y_{1} - \frac{51}{2}$ ,
$a = \frac{1}{4}$
then the given parabola has vertex at
$(x_{1}, x_{2}) \equiv (- \frac{7}{2}, - \frac{51}{2})$
focus at
$(x_{1}, y_{1} + a) \equiv (- \frac{7}{2}, - \frac{101}{4})$
Points of intersection of parabola:
$y = x^{2} + 7 x - 1$
with x-axis where $y = 0$ are
$(\frac{- 7 + \sqrt{53}}{2}, 0) & (\frac{- 7 - \sqrt{53}}{2}, 0)$
and the point of intersection with y-axis is $(0, - 1)$
Now, locate the vertex $&$ locus $&$ draw the axis of parabola. Draw free hand curve passing through above points of intersection with the coordinate axes

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