If the roots are ` (-3,9)`, then the highest/lowest value of y will be attained at x equal to

Options

A. A)`-27`
B. B)6
C. C)`-3`
D. D)3

Answer

To find the x-value at which the highest or lowest value of y will be attained given the roots (-3, 9), we can follow these steps:

### Step 1: Understand the roots
The roots of the quadratic equation are given as α = -3 and β = 9.

### Step 2: Use the formula for the axis of symmetry
The x-coordinate of the vertex (which gives the highest or lowest value of y) can be found using the formula:
\[ x = \frac{\alpha + \beta}{2} \]

### Step 3: Substitute the values of the roots
Now, we substitute the values of α and β into the formula:
\[ x = \frac{-3 + 9}{2} \]

### Step 4: Calculate the sum of the roots
Calculate the sum:
\[ -3 + 9 = 6 \]

### Step 5: Divide by 2
Now, divide the sum by 2:
\[ x = \frac{6}{2} = 3 \]

### Conclusion
Thus, the highest or lowest value of y will be attained at \( x = 3 \).

### Final Answer
The answer is \( x = 3 \).

---