Question

Find the x and y intercepts of f(x)=3x²−4x−3. If f(x)=3x²−4x−3 (to find x, set it to zero), the equation becomes:

3x²−4x−3=0
What are the solutions for x?

A. x=2,13
B. x=−2,13
C. x=−2,−13
D. x=2,−13

Answer 1

The x-intercepts of the given quadratic equation are approximately x = 2 and x = -1.5. The y-intercept is approximately y = -3.

Step-by-step explanation:

To find the x-intercepts, we set f(x) equal to zero:

3x²-4x-3=0

Now we can solve this quadratic equation using factoring or the quadratic formula:

Using the quadratic formula, we have:

x = (-b ± √(b²-4ac)) / (2a)

Plugging in the values a = 3, b = -4, and c = -3, we get:

x = (4 ± √((-4)²-4(3)(-3))) / (2(3))

Simplifying further, we have:

x = (4 ± √(16+36)) / 6

x = (4 ± √52) / 6

Therefore, the x-intercepts are approximately x = 2 and x = -1.5.

To find the y-intercept, we plug in x = 0 into the equation:

f(0) = 3(0)² - 4(0) - 3

f(0) = -3

Therefore, the y-intercept is approximately y = -3.