To determine the value of m for which the quadratic equation y = 18x² + mx + 2 has exactly one x-intercept, we need to consider the nature of the roots of the equation.
A quadratic equation will have exactly one x-intercept if its discriminant is equal to zero. The discriminant (D) for a quadratic equation in the form ax² + bx + c = 0 is calculated as:
D = b² – 4ac
In our equation, a = 18, b = m, and c = 2. Plugging these values into the discriminant formula gives:
D = m² – 4(18)(2)
Calculating the constants:
D = m² – 144
For the graph to have exactly one x-intercept, we set the discriminant to zero:
m² – 144 = 0
Now, solving for m, we can add 144 to both sides:
m² = 144
Taking the square root of both sides, we find:
m = 12 or m = -12
Thus, the values of m for which the graph of y = 18x² + mx + 2 has exactly one x-intercept are m = 12 and m = -12.