Questions: 1. Does the parabola open up or down?
Concave up
Concave down
2. Is the vertex a maximum or a minimum?
Maximum
Minimum
3. What is the y-intercept? Write answer as an (x, y) ordered pair.
4. What is the x coordinate of the vertex? Hint: use formula x=-b/(2a)
What is the y coordinate of the vertex?
Hint: Substitute (plug in) the x coordinate you found for the vertex into the original equation.
Transcript text: 1. Does the parabola open up or down?
Concave up
Concave down
2. Is the vertex a maximum or a minimum?
Maximum
Minimum
3. What is the $y$-intercept? Write answer as an $(x, y)$ ordered pair.
4. What is the x coordinate of the vertex? Hint: use formula $x=\frac{-b}{2 a}$
What is the $y$ coordinate of the vertex?
Hint: Substitute (plug in) the $x$ coordinate you found for the vertex into the original equation.
Solution
Solution Steps
Solution Approach
To determine if the parabola opens up or down, examine the coefficient of the x2 term. If it is positive, the parabola opens up; if negative, it opens down.
To determine if the vertex is a maximum or minimum, use the result from step 1. If the parabola opens up, the vertex is a minimum; if it opens down, the vertex is a maximum.
The y-intercept is found by evaluating the function at x=0.
Step 1: Determine the Direction of the Parabola
The coefficient of the x2 term in the function f(x)=2x2+4x−5 is a=2, which is positive. Therefore, the parabola opens upwards.
Step 2: Identify the Vertex Type
Since the parabola opens upwards, the vertex represents a minimum point.
Step 3: Calculate the y-Intercept
To find the y-intercept, we evaluate the function at x=0:
f(0)=2(0)2+4(0)−5=−5
Thus, the y-intercept is the point (0,−5).
Final Answer
The parabola opens upwards, the vertex is a minimum, and the y-intercept is (0,−5). Therefore, the answers are: