the equation of a curve is given as y+4=(x-1)^2. State the x and y intercepts of the curve
To find the x-intercept of the curve, we set y = 0 in the equation and solve for x.
0 + 4 = (x - 1)^2
4 = (x - 1)^2
Taking the square root of both sides, we get:
±√4 = ±(x - 1)
±2 = ±(x - 1)
Simplifying, we have two possible values for x:
x - 1 = 2 => x = 3
x - 1 = -2 => x = -1
So, the x-intercepts of the curve are x = 3 and x = -1.
To find the y-intercept of the curve, we set x = 0 in the equation and solve for y.
y + 4 = (0 - 1)^2
y + 4 = 1
So, the y-intercept of the curve is y = -3.
The x-intercepts are x = 3 and x = -1, and the y-intercept is y = -3.
To find the x-intercept of the curve, we need to set y = 0 and solve for x.
Let's substitute y = 0 into the equation:
0 + 4 = (x - 1)^2
Simplifying, we get:
4 = (x - 1)^2
Taking the square root of both sides, we have:
2 = x - 1
Adding 1 to both sides, we find:
x = 3
Therefore, the x-intercept of the curve is 3.
To find the y-intercept of the curve, we need to set x = 0 and solve for y.
Let's substitute x = 0 into the equation:
y + 4 = (0 - 1)^2
Simplifying, we get:
y + 4 = 1^2
y + 4 = 1
Subtracting 4 from both sides, we find:
y = -3
Therefore, the y-intercept of the curve is -3.