find x-intercept
-0.01x^2+0.7x+6.1
check your typing, to find the x-intercept I expected to see an equation in x and y.
find x intercept;
y=-0.01x^2+0.7x+6.1
x-intercept occurs when y = 0, thus substitute zero value to y:
0 = -0.01x^2 + 0.7x + 6.1
since this is not factorable, use the quadratic formula:
x = [-b +- sqrt(b^2 - 4*a*c)]/(2*a)
note: +- is plus or minus
where a = -0.01, b = 0.7 and c = 6.1
substitute these values and solve for x.
To find the x-intercept of a quadratic equation, you need to set the equation equal to zero and solve for x. In this case, the given equation is:
-0.01x^2 + 0.7x + 6.1 = 0
Unfortunately, this equation cannot be solved easily by factoring, so we'll have to use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
By comparing this formula to our equation, we can identify the values of a, b, and c:
a = -0.01
b = 0.7
c = 6.1
Plugging these values into the quadratic formula, we get:
x = (-0.7 ± √(0.7^2 - 4 * (-0.01) * 6.1)) / (2 * (-0.01))
Simplifying further:
x = (-0.7 ± √(0.49 + 0.244)) / (-0.02)
x = (-0.7 ± √0.734) / (-0.02)
Now we can find the two possible values for x by evaluating the expression inside the square root:
x = (-0.7 + √0.734) / (-0.02) and x = (-0.7 - √0.734) / (-0.02)
Calculating these expressions, we get:
x = (-0.7 + 0.856) / (-0.02) and x = (-0.7 - 0.856) / (-0.02)
Simplifying further:
x = 0.156 / (-0.02) and x = -1.556 / (-0.02)
The final results are:
x = -7.8 and x = 77.8
Therefore, the x-intercepts of the given equation -0.01x^2 + 0.7x + 6.1 are -7.8 and 77.8.