Hi,
can someone help me with intercepts.
find the intercepts of
f(x) = x^2 - 6x - 2
can someone show how to work this problem.
thanks.
F(x)= Y = X^2 - 6X - 2.
X-Intercepts = The solution = The points where the graph crosses the X-axis.
Use the Quadratic formula to solve the
Eq:
X = (6 +- sqrt((-6)^2+4*1*2)) / 2,
X = (6 +- sqrt(36+8)) / 2,
X = (6 +- 6.632) / 2,
X = (6 + 6.632) / 2 = 6.316.
X = (6 - 6.632) / 2 = -0.-0.316.
Solution set: X = 6.316, and -0.316 =
X-Intercepts
In the given Eq, substitute 0 for X:
Y = 0^2 - 6*0 - 2 = -2 = Y-Int.
Of course! I'd be happy to help you with finding the intercepts of the function f(x) = x^2 - 6x - 2.
To find the x-intercepts, you need to set f(x) = 0 and solve for x. This can be done by factoring, completing the square, or using the quadratic formula.
Let's go through the steps using the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, the equation is x^2 - 6x - 2 = 0, which means a = 1, b = -6, and c = -2.
Plugging these values into the quadratic formula, we get:
x = (-(-6) ± √((-6)^2 - 4 * 1 * (-2))) / (2 * 1)
= (6 ± √(36 + 8)) / 2
= (6 ± √(44)) / 2
= (6 ± 2√11) / 2
Simplifying further, we have:
x = (6 + 2√11) / 2
= 3 + √11
x = (6 - 2√11) / 2
= 3 - √11
So, the x-intercepts of the function f(x) = x^2 - 6x - 2 are x = 3 + √11 and x = 3 - √11.
To find the y-intercept, you need to substitute x = 0 into the equation and solve for y (or f(x)). Let's do that:
f(x) = x^2 - 6x - 2
f(0) = (0)^2 - 6(0) - 2
= 0 - 0 - 2
= -2
Therefore, the y-intercept of the function f(x) = x^2 - 6x - 2 is y = -2.
I hope this explanation helps you understand how to find the intercepts of a quadratic function. Let me know if you have any further questions!