find the intercept of
y=4x^2+3
The intercept of which axis?
y can never be less than 3, so the curve never crosses the x axis.
When x = 0 (where it crosses the y axis), y = 3.
so are those the answers for the x and y intercept
yes. Y intercept is when x=0, it is where it crosses the y axis (x is zero).
X intercept is when y is zero, along the x axis. These are commonly used to find roots of equations.
To find the intercepts of the given quadratic equation, you need to determine the x-intercept(s) and the y-intercept.
1. x-intercept: The x-intercept(s) are the point(s) where the graph of the equation crosses the x-axis, which means the y-coordinate is zero (y=0).
To find the x-intercept(s), substitute y=0 in the equation:
0 = 4x^2 + 3
Now, solve the equation for x. We can use factoring or the quadratic formula to find the solutions:
Using factoring:
0 = 4x^2 + 3
-3 = 4x^2
-3/4 = x^2
Taking the square root of both sides:
±√(-3/4) = x
x = ± (√3)/2
So, the x-intercepts are x = (√3)/2 and x = - (√3)/2.
2. y-intercept: The y-intercept is the point where the graph of the equation crosses the y-axis, which means the x-coordinate is zero (x=0).
To find the y-intercept, substitute x=0 in the equation:
y = 4(0)^2 + 3
y = 0 + 3
y = 3
So, the y-intercept is y = 3.
In summary, the intercepts of the given equation y = 4x^2 + 3 are:
x-intercepts: x = (√3)/2 and x = - (√3)/2
y-intercept: y = 3