Sandra wrote p(x) = 30x + 5x2 in vertex form. her work is below. 1. p(x) = 5x2 + 30x 2. p(x) = 5(x2 + 6x) 3. = 9; 4. p(x) = 5(x2 + 6x + 9) – 5(9) 5. p(x) = 5(x + 3)2 – 45 describe sandra’s function. what is the vertex of this function? is it a maximum or a minimum? what is the axis of symmetry of this function?

1)

We are given a equation p(x) which is given as:

Sandra's function is a quadratic function whose graph is  a upward open parabola with vertex at (-3,-45).

2)

We know that the vertex of a equation of the type:

is (h,k)

We have the equation as:

Hence, the vertex is:

(-3,-45).

3)

As the parabola is a upward open parabola hence, the parabola has a minimum value but not the maximum values as the function is unbounded above.

Hence, the vertex is a minimum.

4)

The axis of symmetry of a parabolic function is  a line which act as a mirror for the parabola.

We know that for the general equation of the type:

The axis of symmetry is:

We have a=5 and b=30

Hence, the axis of symmetry is:

Hence, axis of symmetry is:

x= -3

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490