Question

the function $g(x) = 10x^2 - 100x + 213$ written in vertex form is $g(x) = 10(x - 5)^2 - 37$. which statements are true about $g(x)$? choose three correct answers. the parabola opens up. the axis of symmetry is the line $x = -5$. the parabola has a minimum.

Explanation:

Step1: Check parabola direction

Vertex form: $g(x)=a(x-h)^2+k$, $a=10>0$, so parabola opens up.

Step2: Find axis of symmetry

Axis of symmetry is $x=h$, here $h=5$, so $x=5$.

Step3: Check for min/max

Since $a>0$, parabola opens up, so it has a minimum.

Answer:

• The parabola opens up.
• The parabola has a minimum.

(Note: The statement "The axis of symmetry is the line $x=-5$" is false; the correct axis is $x=5$.)