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.
the axis of symmetry is the line x = –5.
the vertex of the graph is (5, –37).
the parabola has a minimum.
the parabola opens up.
the value of a, when the equation is written in vertex form, is negative.

The true statements are:-

The vertex of the graph is (5, –37).

The parabola has a minimum.

The parabola opens up.

Step-by-step explanation:

We know that for the standard vertex form , where(h,k) is the vertex of the curve.

Given function:- written in vertex form

The a=10 which is not negative.

⇒It is a equation of parabola open upwards.

On comparing it with standard vertex form, we get vertex (h,k)=(5,-37)

The axis of symmetry is the line x=5

We know that if then its minimum value is at

⇒Parabola has minimum value.

7.6 m/s faster

Step-by-step explanation:

Speed of swimmer = 1.8 meters per second

The distance covered by runner = 200

Time of runner = 21.3 sec

We have to find the speed of the runner first so that we can compare with the speed of swimmer.

Speed = Distance/Time

=> 200/21.3

=> 9.4 m/s

So we have to find the difference between both speeds

Difference = 9.4 - 1.8

=> 7.6 m/s

So the runner was 7.6 m/s faster..