Question

Find the x
-intercept(s) and the coordinates of the vertex for the parabola
Y= x^2 + 6x - 7
. If there is more than one x-intercept, separate them with commas.

Answer 1

So basically I find the vertex using the equation and then plot two points on either side of the vertex and then just find the x intercept of each point? @

Answer 2

@jdoe0001

Answer 3

well, the x-intercepts is where the graph touches the x-axis
at that point, y = 0
so if you set that to 0, and solve "x", by factoring
you should be able to get the "solutions"

\(\bf 0 = x^2 + 6x - 7\)

unless you're asked to graph it

Answer 4

and yes, you could do it like the previous one as well
get the vertex, a couple of points on either side, to get the x-intercepts or solutions

Answer 5

\(\bf y= x^2 + 6x - 7
\\ \quad \\
\textit{vertex of a parabola}\\ \quad \\
y = {\color{red}{ 1}}x^2{\color{blue}{ +6}}x{\color{green}{ -7}}\qquad

\left(-\cfrac{{\color{blue}{ b}}}{2{\color{red}{ a}}}\quad ,\quad {\color{green}{ c}}-\cfrac{{\color{blue}{ b}}^2}{4{\color{red}{ a}}}\right)\)

Answer 6

ok cool so I guess my only question now is how do you know how the equation plugs in to the other one like that?

Answer 7

hmmm what do you mean?

Answer 8

like when you color code the equation I post so I know where to plug it in at, how do you know that's where they plug in at? oh and I got (3,-2) btw

Answer 9

ohhh is a notation, or formula based on the pattern of the values

Answer 10

well
\(\bf \left(-\cfrac{{\color{blue}{ 6}}}{2{\color{red}{ (1)}}}\quad ,\quad {\color{green}{ -7}}-\cfrac{{\color{blue}{ 6}}^2}{4{\color{red}{ (1)}}}\right)\implies \left( -3,-7-\cfrac{\cancel{36}}{\cancel{4}} \right)
\\ \quad \\
\left( -3, -7-9 \right)\)

Answer 11

ohh yeahh nope definitely got that wrong.. thank you though!

Answer 12

yw