Question

Determine the direction the parabola opens and the y-intercept for the function

Answer 1

$\begin{gathered} (a)\text{upwards } \\ (b)\text{y-intercept is -6} \end{gathered}$

Explanation

Step 1

Given

$y=ax^2+bx+c$

If a > 0 (positive) then the parabola opens upward.

If a < 0 (negative) then the parabola opens downward.

Hence

$\begin{gathered} ax^2+bx+c\rightarrow3x^2+9x-6 \\ therefore \\ a=3 \end{gathered}$

it means, the parabola opens upward

Step 2

x-intercept:

The y-intercept of any graph is a point on the y-axis and therefore has x-coordinate 0.

$\begin{gathered} y=3x^2+9x-6 \\ at\text{ x=0} \\ y=3(0)^2+9(0)-6 \\ y=-6 \\ so\text{, the y-intercept is -6} \end{gathered}$

I hope this helps you

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