Question

My course is asking me to solve a quadratic equation graphically. I know that this is a pretty bass-ackwards method of "solving."
The equation is 7x+3=5x^2

Answer 1

First, I reformed it into \[5x^2-7x-3\]

Answer 2

obviously you can tell this is a prabola that opens up ward

Answer 3

Now i believe that if you find the vertex or even just the x intecepts, taht should be enough to distinguish which is the correct graph of this quadratic

Answer 4

i ended up with \[(7\pm \sqrt{109})/10\]

Answer 5

Well, it is asking for the zeros. I should be able to determine this algebraically, right?
I came up with 1.744, -.344

Answer 6

yeah that looks right

Answer 7

i entered that answer, and it said that the correct answer was -.344, 1.744

Those two numbers are the x intercepts, correct? If that is so, I'm assuming that I just need to order them from left to right.

How do I determine the correct order? also, how do I determine the vertex?

Answer 8

Well, consider this

So, then you should write it from left to right

Answer 9

the vertex you can determine by completing the square

Answer 10

can you do that on your own or do you want some help?

Answer 11

Hmm... let's see. Completing the square. I don't remember how to do that. I do remember that there was another method for finding the vertex, a simple equation...

Answer 12

So, I would like some help with completing the square, but if you know the equation that would be better

Answer 13

-b/2a is the formula you can use to find the x-value of the vertex of this parabola, then simply plug that x-value back into the orginal function to find the y value of the vertex

Answer 14

thanks! I was looking through an old notebook, trying to find that equation.

Answer 15

so the vertex would be (3/5), -2.2?

Answer 16

oops, that is for a different equation.

Answer 17

so, .7,-5.45?

Answer 18

thats right

Answer 19

Thanks!