Question

How can I go about this? This is one of the questions in the BlueBook Digital SAT practice questions. I used vertex form but it didn't work.

Answer 1

Answer:

-12

Step-by-step explanation:

From the vertex form,

$\displaystyle{y=a(x-h)^2+k}$

Since the vertex is at (9,-14). Therefore,

$\displaystyle{y=a(x-9)^2-14}$

Since the question says that it intersects x-axis at two points. This means that a > 0 or a-term can only be positive value. This is because if a-term is negative, the parabola will be upward and it'll not intersect any x-axis at all. (See attachment below)

Now let's try expand and form the standard equation:

$\displaystyle{y=ax^2-18ax+81a-14}$

If we sum a, b and c together, we will have:

$\displaystyle{a+(-18a)+(81a-14) = a-18a+81a-14}\\\\\displaystyle{=64a-14}$

So let's say, if a = 0, it's -14 right? However, a = 0 cannot be used because parabola is defined that a ≠ 0.

And we know that for each positive increasing a-value, the sum will continue to grow higher and higher.

This means that we have to find the number that is greater than -14 itself, which is -12.

Hence, the sum a + b + c could be -12.