Graph the quadratic function. f (x) = - x² - 3x + 2

Question

Quizplus · Accepted Answer

The given quadratic function is in standard form: f(x) = ax^2 + bx + c, where a = -1, b = -3, and c = 2.
To graph the function, we first need to find the vertex of the parabola, which is given by (-b/2a, f(-b/2a)). 
In this case, the vertex is (3/2, 25/4). 
Next, we can plot this vertex on the coordinate plane.
Since the coefficient of x^2 is negative, the parabola will open downwards. 
To determine the shape and position of the parabola, we can find the x-intercepts (if any) and the y-intercept. 
To find the x-intercepts, we need to solve the quadratic equation -x^2 - 3x + 2 = 0. 
Using the quadratic formula, we get x = (-b ± sqrt(b^2 - 4ac))/2a. 
Plugging in the values of a, b, and c, we get x = (-(-3) ± sqrt((-3)^2 - 4(-1)(2)))/(2(-1)) = (-3 ± sqrt(17))/(-2). 
Therefore, the x-intercepts are approximately -0.56 and 3.56. 
To find the y-intercept, we need to find f(0), which is equal to 2. 
Thus, the y-intercept is (0, 2). 
Using this information, we can sketch the graph of the parabola, as shown in choice C.

Graph the Quadratic Function