Parabola defined by the equation y = -x² - 3x + 6 will be represented by the picture attached.
Equation of the parabola given in the question is,
y = -x² - 3x + 6
Convert this equation in the vertex form, [y = a(x - h)² + k, here (h, k) is the vertex of the parabola]
y = -x² - 2(1.5)x - (1.5)² + (1.5)² + 6
= -(x + 1.5)²+ (1.5)² + 6
= -(x + 1.5)² + 2.25 + 6
= -(x + 1.5)² + 8.25
From this equation vertex of the parabola will be (-1.5, 8.25).
Leading coefficient 'a' = -1 (negative)
y - intercept of the equation → y = -(0 - 1.5)² + 8.25
y = 6
x- intercept of the equation → 0 = -(x - 1.5)² + 8.25
(x - 1.5) = √8.25
x = 1.372, -4.372
Therefore, parabola will open downwards (a is negative), y-intercept (0, 6) and x-intercepts as (-4.372, 0), (1.372, 0) and vertex as (1.5, 8.25).
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