Consider the quadratic function f(x) = -x^2 + 1x + 12. determine the following: (enter all numerical answers as integers, fractions, or decimals): the smallest -intercept is 2 = the largest x-intercept is z = the y-intercept is y = the vertex is ( the line of symmetry has the equation preview

Answer and Explanation:

Given : The quadratic function

To find : Determine the following ?

Solution :

The x -intercept are where f(x)=0,

So,

Applying middle term split,

The x-intercepts are (4,0) and (-3,0).

The smallest x-intercept is x=-3

The largest x-intercept is x=4

The y -intercept are where x=0,

So,

The y-intercept is y=12.

The quadratic function is in the form,

On comparing, a=-1 , b=1 and c=1 2

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

For k, The y-coordinate of the vertex is given by,

The vertex of the function is

The x-coordinate of the vertex i.e. is the axis of symmetry,

So, (solved above)

The axis of symmetry is .