can you help me find the x and y intercepts and the T.P of this equation?

Question

the question is y = -xsquared + 2x + 1. I cannot work out my x intercept..can you help?

Answer 1

Homework question.
Your x and Y intercepts:
Y = -X^2 + 2X + 1.

Remember, your intercepts are where the line for the equation crosses the graphical X and Y lines meaning when X = 0 or when Y = 0.
So set them so.
to Find Y intercept set X to Zero.
Y = -(0)^2 + 2(0) + 1
Y = 1 (when X = 0)
Y intercept is (0,1).

to find X intercept set Y to Zero
(0) = -X^2 + 2X + 1
or
0 = (-1)X^2 + (2)X + (1)

Get your quadratic equation out.
X = (-b (+ -) SQRT(b^2 - 4ac)) / 2a
and you will get your answer
You should get something like
X can be either:
(-2 + SQRT(8))/ -2

or
(-2 - SQRT(8))/ 2

Hope this helps, and remember (or memorize) the quadratic equation.. it will save you more than once.

Answer 2

the x intercepts are the two places where this intersects the x-axis, that is where y=0

substitute y = 0 into your equation:
0 = -x^2 +2*x +1

You are looking for the roots of the equation, and you should know how to get that.

The numerical answers are -0.4142 and 2.4142.
In matlab thats roots([-1 2 1])

Answer 3

x intercept: -x^2+2x+1=0
rewrite it like this: -(x^2-2x-1)=0
so the x-intercepts of the original equation are the same as the x-intercepts of x^2-2x-1=0
now for this you use the quadratic formula to get:
[2+square root of (8) ]/2 and
[2-square root of (8) ]/2

Answer 4

Using the quadratic formula, the two roots are 1+sqrt2 and 1-sqrt2. [ 2.414 and -0.414]

The roots are the x intercepts.
When x=0, y=1. Thats the y intercept.

Answer 5

y = -x^2 + 2x + 1
y = -(x^2 - 2x - 1)

x = (-b ± sqrt(b^2 - 4ac))/(2a)
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-1)))/(2(1))
x = (2 ± sqrt(4 + 4))/2
x = (2 ± sqrt(4(2)))/2
x = (2 ± 2sqrt(2))/2
x = 1 ± sqrt(2)

x-intercepts are 1 + sqrt(2) and 1 - sqrt(2)
y-intercept is 1

I don't know what you mean by TP, but the vertex is

x = (-2)/(2(-1))
x = -2/(-2)
x = 1

y = -(1)^2 + 2(1) + 1
y = -1 + 2 + 1
y = 1 + 1
y = 2

V : (1,2)