Question

Points A, B, C, D, E, F, and G lie on the graph of function g( x ) as shown on the coordinate grid.

All the coordinates of the marked points are integers. Drag and drop numbers into the boxes to complete each form of the function
numbers to boxes:
-5, 0, 3, 4, 5, 6, 7

Answer 1

`g(x)=-(x-5)^2+4\\=-(x-7)(x-3)`

Explanation:

Given: coordinate grid

To find: the missing number

Solution:

Equation of the parabola that open downwards and is symmetric about y-axis is
`(x-h)^2=-4p(y-k)` where
`(h,k)` denotes the vertex and focus is at
`(h,k+p)`

`g(x)=-(x-.....\,\,\,\,)^2+\left ( ....... \right )\\(x-.....\,\,\,\,)^2=-\left ( g(x)-(....) \right )`

`(x-h)^2=-\left ( g(x)-(k) \right )`

From the graph, vertex is
`(5,4)`. Put
`(h,k)=(5,4)`

`g(x)=-(x-5)^2+4\\=-\left [ (x-5)^2-2^2 \right ]`

Use formula
`a^2-b^2=(a+b)(a-b)`

So,

`g(x)=-\left [ (x-5)^2-2^2 \right ]\\=-\left [ (x-5-2)(x-5+2) \right ]\\=-(x-7)(x-3)`