The graph of the quadratic $y = ax^2 + bx + c$ is a parabola that passes through the points $(-1,7)$, $(5,7)$, and $(6,10)$. what is the $x$-coordinate of the vertex of the parabola?

Two of the given points have the same y-value. The midpoint of those two will be on the line of symmetry, as is the vertex. The x-value there is (-1+5)/2 = 2.

Step-by-step explanation:

Let consider the following linear equation systems by using the known points and second-grade polynomial:

(-1, 7)

(5, 7)

(6,10)

After some algebraic manipulation, the values for the polynomial coefficients are found:

, ,

The polynomial is:

Lastly, the vertex is found by further handling:

The coordinates for the vertex are:

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

answer is 144

step-by-step explanation: