Needed help with this math question.

Question

y= 4x^2 +6x - 2

Using the quadratic formula to identify any x-intercepts on the graph of this equation x=? or are there no x- intercepts?

Answer 1

y = ax² + bx + c
To find zeros of the quadratic function use formula:
x₁₂ = (- b ± √D) / (2a) , D = b² - 4ac
In the set of real numbers:
1. There are two zeros, if D > 0
2. There is one zero, if D = 0
3. There is no zeros, if D < 0
Let's find value of x if y = 0
4x² + 6x - 2 = 0 ---> 2x² + 3x - 1 = 0
D = 3² - 4*2*(-1) = 17 > 0
x₁ = (-3 + √17) / 4
x₂ = (-3 - √17) / 4

Answer 2

Adding to what Mark said, you can graph the equation too (either by hand or with the aid of a graphing calculator) to check that what you have solved using the Quadratic equation is correct. You'll be able to see if and where the function crosses the x-axis.

Answer 3

Just a hint but the x-intercept is where the graph crosses the x-axis so ask yourself what value does "y" have when this occurs.  You can directly use the Quadratic equation and solve for values of x for this special case.  If the values are real numbers then they exist.