Answer:
To find the x-intercepts, we need to set f(x) to 0 and solve for x:
2x² + 5x + 2 = 0
We can factor this quadratic equation:
(2x + 1)(x + 2) = 0
This gives us two solutions:
2x + 1 = 0 or x + 2 = 0
Solving for x, we get:
x = -1/2 or x = -2
Therefore, the x-intercepts are (-1/2, 0) and (-2, 0).
To find the y-intercept, we need to set x to 0:
f(0) = 2(0)² + 5(0) + 2 = 2
Therefore, the y-intercept is (0, 2).
To graph the function, we can plot the x- and y-intercepts and sketch the parabola using symmetry:
- The vertex of the parabola is at x = -b/2a = -5/4 and y = f(-5/4) = -3/8.
- The axis of symmetry is x = -5/4.
- The parabola
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Answers & Comments
Answer:
To find the x-intercepts, we need to set f(x) to 0 and solve for x:
2x² + 5x + 2 = 0
We can factor this quadratic equation:
(2x + 1)(x + 2) = 0
This gives us two solutions:
2x + 1 = 0 or x + 2 = 0
Solving for x, we get:
x = -1/2 or x = -2
Therefore, the x-intercepts are (-1/2, 0) and (-2, 0).
To find the y-intercept, we need to set x to 0:
f(0) = 2(0)² + 5(0) + 2 = 2
Therefore, the y-intercept is (0, 2).
To graph the function, we can plot the x- and y-intercepts and sketch the parabola using symmetry:
- The vertex of the parabola is at x = -b/2a = -5/4 and y = f(-5/4) = -3/8.
- The axis of symmetry is x = -5/4.
- The parabola