Graph the equation $y = - 0.5 x ^ { 2 } + 1.5 x + 10$ .

Question

Quizplus · Accepted Answer

To graph the equation, we can start by finding the vertex of the parabola. 
The x-coordinate of the vertex can be found using the formula: 
x = -b/2a
where a and b are the coefficients of the x-term and x-squared term, respectively. In this case, a = -0.5 and b = 1.5, so:
x = -1.5/(-1) = 1.5
The y-coordinate of the vertex can be found by plugging in the x-coordinate into the equation:
y = -0.5(1.5)^2 + 1.5(1.5) + 10 = 11.25
So the vertex is at (1.5, 11.25). 
Next, we can plot a few more points to get an idea of the shape of the parabola. We can choose some values of x, plug them into the equation, and find the corresponding y-values. For example:
when x = 0,
y = -0.5(0)^2 + 1.5(0) + 10 = 10
when x = 2,
y = -0.5(2)^2 + 1.5(2) + 10 = 9
when x = -2,
y = -0.5(-2)^2 + 1.5(-2) + 10 = 13
We can plot these points and connect them with a smooth curve to get the graph of the parabola. The correct choice is C.

Graph the Equation y=−0.5x2+1.5x+10y = - 0.5 x ^ { 2 } + 1.5 x + 10y=−0.5x2+1.5x+10

Graph the Equation $y = - 0.5 x ^ { 2 } + 1.5 x + 10$