find the x- intercepts?

Question

find the x-intercepts and the coordinates of the vertex for the parabola y=x^2 - 2x - 15. If there is more than one x-intercept than write them all.

Answer 1

The x intercepts are (5,0) and (-3, 0)
The vertex is (1, -16)

You can find the x intercepts simply by factoring the equation
y=x^2-2x-15
y=(x-5)(x+3) (negative five * three equals -15, the constant - coefficient; -5 + 3 equals -2, the linear
- coefficient)

Next y is set to equal zero because x intercepts' y coordinate is always zero; thus:
0=(x-5)(x+3)

Now because the right side of the equation equals zero, it means one or both units expressions in parenthesis equals zero. We show this by the following two equations:
x - 5 = 0 and x + 3 = 0
+ 5 + 5 and - 3 - 3
------------------------------------------
x = 5 and x = -3 (This gives us the x - intercepts)




To get the axis of symmetry we use the equation x = (-b) / 2a
plugging in the variables we get x = (--2) / 2(1)
This becomes x = 2/2 or x = 1.
Thus the x coordinate of the axis of symmetry is:
x = 1.

We plug this into the equation
y = x^2 - 2x - 15 and get y = (1)^2 - 2(1) - 15.
Solving that equation we get:
y = 1 - 2 - 15
y = -1 - 15
y = -16 (this is the y coordinate of the AoS)

This places the axis of symmetry of this parabola at (1, -16)

hmm, yep sounds 'bout right...

Answer 2

to find the x intercepts solve the equation for x with y=0

0=x^2 -2x -15 = (x-5)(x+3)
x-5 = 0 and x+3 = 0
the intercepts are x=5, x=-3

to find the vertex take the derivative of the expression and set it equal to zero and solve for x. this will give the maximum or minimum value of x which will be the vertex. put this value back into the original equation and solve for y.

dy/dx = 2x -2 = 0
x = 1 this is obvious correct because it lies halfway between the intercepts which it must because the vertex is on the axis of symmetry.

now using original equation y =1^2 -2(1) -15 = -16

the vertex is, therefore, x=1,y=16

Answer 3

first of all, there can only be on x intercept because the x intercept in the linear equation is where the line passes through the x axis. The x intercept is x^2-15-y.

Answer 4

This can be factored easily enough.

0 = x^2 - 2x - 15
0 = (x - 5)(x + 3)
x = {-3, 5}

Answer 5

x-5 and x+ 3

5 and -3

factor