11. What are the x-intercepts of the graph of the quadratic function f(x) = 5x2 + 4x – 1?
well,
f(x) = (5x-1)(x+1)
when is that zero?
To find the x-intercepts of the graph of the quadratic function f(x) = 5x^2 + 4x - 1, you need to set f(x) equal to zero and solve for x.
So, we have the equation:
5x^2 + 4x - 1 = 0
To solve this equation, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 5, b = 4, and c = -1.
Plugging these values into the quadratic formula, we get:
x = (-4 ± √(4^2 - 4*5*(-1))) / (2*5)
x = (-4 ± √(16 + 20)) / 10
x = (-4 ± √36) / 10
x = (-4 ± 6) / 10
Now, we can simplify the solution:
x = (-4 + 6) / 10 = 2/10 = 1/5
x = (-4 - 6) / 10 = -10/10 = -1
So, the x-intercepts of the graph of the quadratic function f(x) = 5x^2 + 4x - 1 are 1/5 and -1.
To find the x-intercepts of the graph of a quadratic function, you need to solve the equation f(x) = 0. In this case, the quadratic function is f(x) = 5x^2 + 4x - 1.
To solve for x, set the equation equal to zero:
5x^2 + 4x - 1 = 0
Now, you can use the quadratic formula to find the x-intercepts. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a, b, and c are the coefficients of the quadratic equation:
a = 5
b = 4
c = -1
Plug these values into the quadratic formula and solve for x:
x = (-4 ± √(4^2 - 4(5)(-1))) / (2(5))
Simplifying further:
x = (-4 ± √(16 + 20)) / 10
x = (-4 ± √(36)) / 10
x = (-4 ± 6) / 10
So, we have two possible solutions for x:
x = (-4 + 6) / 10 = 2 / 10 = 0.2
x = (-4 - 6) / 10 = -10 / 10 = -1
Therefore, the x-intercepts of the graph of the quadratic function f(x) = 5x^2 + 4x - 1 are x = 0.2 and x = -1.