Question

Graph the function to find the zeros. Rewrite the function with the polynomial in factored form.

y=2x^2+3x-5
Help....

Answer 1

To graph the function you'd have to find the zeros first, so you'd have to factorise it and then graph it.
Do you know how to factorise a quadratic polynomial?

Answer 2

No.. well i can try :)

Answer 3

Finding the zeros is harder for me to do...

Answer 4

Don't worry, take your time. The quadratic formula might be the easiest way to do it if you know how to do that?

Answer 5

In fact, if you use the quadratic formula to find the zeros then you would be able to graph the function before factorising so I suggest you do that :)

Answer 6

So i use the quadratic formula to find zeros first?

Answer 7

Yes, let me know what you get for the zeros.

Answer 8

okay so would the zeros be 1 and -5/2??
Then i facored it before would it be (2x+5)(x-1)??

Answer 9

Correct and correct :)
Now to graph the function you need the x intercepts (which you have, they are the zeros) and the y intercept. Do you know how to find the y-intercept?

Answer 10

is there a formula for that kind of function?

Answer 11

No, the y-intercept is the easiest thing to find. If you have a quadratic equation then the y-intercept will be the constant (the term which doesn't involve an x).
This is because the y-intercept is the point where x=0. So if we substitute that into the equation we are just left with the constant term. Do you understand?

Answer 12

not quite ...? so the y=mx+b formula is not involved with this?

Answer 13

Not with this no but it's very similar. If you have the equation of a line as y=mx+c, the y-intercept is just the c, right?
For an equation of the form y=ax^2+bx+c, the y-intercept is just the c on the end again.
Please say if you still don't understand, it's no trouble.

Answer 14

Oh okay i see i studied that it is the quadratic in standard form right? but i leatned that in finding 2 numbers that add to give b and multiply to give ac.

Answer 15

Yes that's the standard form of a quadratic equation. I think you're overcomplicating this in your head. You already have the x intercepts: x=1 and x=-5/2.
The y-intercepts are just the c in the standard form of the quadratic equation. All it is is the term in the equation which has no x's with it.
For example, the y-intercept of y=3x^2+4x+2 is 2,
the y-intercept of y=100x^2+77x-15 is 15.
So can you tell me what the y-intercept of your function is?

Answer 16

-5?

Answer 17

Yes indeed :) So now you have all the required information to sketch the graph, and you factorised it yourself. Are there any questions you have about this now or is that ok?

Answer 18

Awesome! so i found the zeros without the graph for now and so when i rewrite the function with the polynomial in factored form it would just be what i factored? right?

Answer 19

Yes your factored form of y=(2x+5)(x-1) was correct.

Answer 20

Great! Thank you for all your help i think i can get the graph from here. :) Thank you so so much!

Answer 21

Not a problem, good luck with your studies!

Answer 22

Thank you!