Use a graphing calculator to find the y-intercept and x-intercepts of the function
y = 0.5x^2 + 2x + 1
A. y-intercept: -1; x-intercepts: -3.414 and -0.586
B. y-intercept: 1; x-intercepts: -3.414 and -0.586
C. y-intercept: -1; x-intercepts: -3.521 and -0.606
D. y-intercept: 1; x-intercepts: -3.521 and -0.606
To find the y-intercept, we set x = 0 in the equation:
y = 0.5(0)^2 + 2(0) + 1
y = 0 + 0 + 1
y = 1
So the y-intercept is at (0, 1).
To find the x-intercepts, we set y = 0 in the equation and use the quadratic formula. However, since we are using a graphing calculator, we can simply input the equation and find the x-intercepts.
After inputting the equation y = 0.5x^2 + 2x + 1 into a graphing calculator, we find that the x-intercepts are approximately -3.521 and -0.606.
Therefore, the correct answer is:
C. y-intercept: -1; x-intercepts: -3.521 and -0.606