Question

Consider the quadratic f(x)=x^2-2x-3
Find the x-intercepts of the graph of f(x).
I just want to know the formula on how to find the x-intercepts.

Answer 1

To find the x-intercept, you have to plug in y = 0

But it will be easier to find the x-intercept if we factor x^2-2x-3

Answer 2

The factors would be (x-3)(x+1) right?

Answer 3

@MeganXOXO

Answer 4

Correct!

And here's a small property:

ab = 0, if a = 0, or b = 0, or if both a and b equal to 0

So we have

(x-3)(x+1) = 0

x - 3 = 0
x + 1 = 0

solve for x. :)

Answer 5

So the x-intercepts are (3,0) and (-1,0)? @MeganXOXO

Answer 6

Correct! :)

Answer 7

Thank you so much! :) Also to find the y-intercept is -3 because in standard form the c stands for the y-intercept, but I don't know how to figure that out by equation.. Do you know how? @MeganXOXO

Answer 8

Yes, I do! @vpopstar13

Answer 9

To find the y-intercept, you plug in x = 0 and solve for y

So we had

y = (x-3)(x+1)

Plug in x = 0

y = (0-3)(0+1)
y = (-3)(1)
y = -3

(0,-3)

Do you understand? @vpopstar13

Answer 10

Ohhh, yes! Thank you so much again. @MeganXOXO

Answer 11

I'm glad that I could help @vpopstar13 !

Answer 12

I also have one more question... @MeganXOXO

Answer 13

Sure @vpopstar13

Answer 14

The vertex is the y-intercept right? But the problem is saying find the coordinates of the vertex of the graph.. I don't understand what it's saying. @MeganXOXO

Answer 15

Nope @vpopstar13

Answer 16

The vertex is -b/2a

where the equation is ax^2 + bx + c =0

Answer 17

So the vertex is the b in standard form? @MeganXOXO

Answer 18

Wait I am so confused..

Answer 19

Read this: http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

Answer 20

Okay so the formula is a(x-h)^2 + k
I just need to convert my standard form into vertex form, right? @MeganXOXO

Answer 21

You can do that too! :)