The function g(x) = 10x2 – 100x + 213 written in vertex form is g(x) = 10(x – 5)2 – 37. which statements are true about g(x)? check all that apply. 1-the axis of symmetry is the line x = –5. 2-the vertex of the graph is (5, –37). 3-the parabola has a minimum. 4-the parabola opens up. 5-the value of a, when the equation is written in vertex form, is negative.

 The correct options are

(2) The vertex of the graph is (5, –37).

(3) The parabola has a minimum.

(4) The parabola opens up.

Step-by-step explanation: Given that the function is written as follows in the vertex form :

We are to select all the correct options.

We know that

for the STANDARD equation of a parabola, i.e.,

the vertex of the parabola is (h, k),

the parabola has a minimum and opens up if a is positive, the parabola has a maximum and opens down if a is negative.

Comparing the equation (i) with the standard vertex form, we get

the axis of symmetry is given by

The vertex of the parabola will be

(h, k) = (5, -37).

Since the value of a is 10, positive, so the parabola has a minimum and opens up.

Thus, the correct options are

(2) The vertex of the graph is (5, –37).

(3) The parabola has a minimum.

(4) The parabola opens up.