find the x- and y- intercepts
f(x)= 25x^2+10x+1
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The y-intercept is obtained by setting x=0, i.e.
y-intercept=f(0)=1
The x-intercepts is obtained by setting y=0.
In this case,
y=0=25x^2+10x+1=(5x+1)^sup2;
i.e. (5x+1)=0, or x=-(1/5)
To find the x-intercepts of a function, you need to set the function equal to zero and solve for x.
Given the function f(x) = 25x^2 + 10x + 1, set f(x) equal to zero:
0 = 25x^2 + 10x + 1
Now, we can apply the quadratic formula to find the x-intercepts. The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 25, b = 10, and c = 1. Substituting these values into the quadratic formula, we get:
x = (-10 ± √(10^2 - 4 * 25 * 1)) / (2 * 25)
Now we can simplify and calculate the solutions:
x = (-10 ± √(100 - 100)) / 50
x = (-10 ± √0) / 50
x = -10/50
Simplifying further:
x = -1/5
Therefore, the x-intercept is x = -1/5.
To find the y-intercept of a function, substitute x = 0 into the function f(x) and solve for y:
f(0) = 25(0)^2 + 10(0) + 1
f(0) = 0 + 0 + 1
f(0) = 1
Therefore, the y-intercept is y = 1.
In summary, the x-intercept is x = -1/5 and the y-intercept is y = 1 for the function f(x) = 25x^2 + 10x + 1.