Question

a student writes two equations.
equation a: ( y = 3x^2 + 5x - 12 )
equation b: ( y = 2x + 10 )
what is true about the graph of equation a?
( circ ) it is a parabola that opens up with a y - intercept at ( (0, 12) ).
( circ ) it is a parabola that opens up with a y - intercept at ( (0, -12) ).
( circ ) it is a parabola that opens down with a y - intercept at ( (0, 12) ).
( circ ) it is a parabola that opens down with a y - intercept at ( (0, -12) ).

Explanation:

Step1: Identify parabola direction

For quadratic equation $y=ax^2+bx+c$, if $a>0$, parabola opens up. Here $a=3>0$, so opens up.

Step2: Find y-intercept

Set $x=0$ in $y=3x^2+5x-12$:
$y=3(0)^2+5(0)-12=-12$. So y-intercept is $(0,-12)$.

Answer:

It is a parabola that opens up with a y-intercept at (0, -12).