Question

The quadratic function $f\left(x\right)=a{x}^2+bx+c$ is known to pass through the points (-1, 6), (7, 6), and (1, - 6). Find the smallest value of the function.

• A. -6
• B. -10
• C. -20
• D. -26

Answer 1

The correct option is B

-10

If the points (-1,6), (7,6),and (1,-6) lie oh the graph of $y=a{x}^2+bx+c,$
Then 6 = a - b + c, 6 = 49a + 7b + c, -6 = a + b + c.
Solving this system, we get a = 1, b = -6, c = -1.
The graph of f(x) = $x^2-6x-1$ is a parabola that opens upward and the vertex is $(-\frac{b}{2a},-\frac{D}{4a})$=(3,-10).
Option (b).