Question

2. The graph of f(x) = -x² +8x+ 20 is sketched below. The graph intersects the x-axis at (-2;0) and (10;0), and the y — axis at (0; 20). The point (4;36) is the turning point of f. -2 20 0 Y (4:36) 1 10 the a is called th T​

Answer 1

To find the value of p for which the equation -x^2 + 8x + p = 0 has equal roots, we need to use the discriminant of the quadratic formula, which is b^2 - 4ac. If the discriminant is equal to zero, then the equation has equal roots.

In this case, the equation is -x^2 + 8x + p = 0. Comparing this to the standard quadratic equation ax^2 + bx + c = 0, we can see that a = -1, b = 8, and c = p.

To find the discriminant, we can substitute these values into the formula:

b^2 - 4ac = 8^2 - 4(-1)(p) = 64 + 4p

We want this expression to be equal to zero, so we can set it equal to zero and solve for p:

64 + 4p = 0
4p = -64
p = -16

Therefore, the value of p for which -x^2 + 8x + p = 0 has equal roots is -16.