What value of m makes the graph of y = 18x² + mx + 2 have exactly one x-intercept?

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To determine the value of m for which the quadratic equation y = 18x² + mx + 2 has exactly one x-intercept, we need to analyze the conditions under which a quadratic equation has a unique solution. This occurs when the discriminant of the quadratic equation is zero.

The standard form of a quadratic equation is given by:

y = ax² + bx + c

In this case, the coefficients are:

  • a = 18
  • b = m
  • c = 2

Next, the discriminant D for a quadratic equation is calculated using the formula:

D = b² - 4ac

Substituting the values of a, b, and c into the discriminant formula, we have:

D = m² - 4(18)(2)

Calculating the constant term:

D = m² - 144

To find the value of m that gives exactly one x-intercept, we need to set the discriminant equal to zero:

m² - 144 = 0

Solving for m, we can rearrange the equation:

m² = 144

Taking the square root of both sides, we find:

m = ±12

Thus, the values of m that make the graph of y = 18x² + mx + 2 have exactly one x-intercept are m = 12 and m = -12.

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