Question

which equation best matches the graph shown below?
answer
\\( y = -9x^2 + 9x - 1 \\) \\( y = 9x^2 + 9x - 1 \\)
\\( y = 9x^2 + 9x + 1.3 \\) \\( y = -9x^2 + 9x + 1.3 \\)

Explanation:

Step1: Identify parabola direction

The parabola opens downward, so the coefficient of $x^2$ must be negative. This eliminates the options $y=9x^2+9x-1$ and $y=9x^2+9x+1.3$.

Step2: Find y-intercept

The graph crosses the y-axis at a positive value (between 0 and 2). For a quadratic $y=ax^2+bx+c$, the y-intercept is $c$.

• For $y=-9x^2+9x-1$, $c=-1$ (negative, does not match).
• For $y=-9x^2+9x+1.3$, $c=1.3$ (positive, matches the graph).

Answer:

$y = -9x^2 + 9x + 1.3$