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.

Solution Steps

1. To determine if the parabola opens up or down, examine the coefficient of the \(x^2\) term. If it is positive, the parabola opens up; if negative, it opens down.
2. 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.
3. The \(y\)-intercept is found by evaluating the function at \(x = 0\).

The coefficient of the \(x^2\) term in the function \(f(x) = 2x^2 + 4x - 5\) is \(a = 2\), which is positive. Therefore, the parabola opens upwards.

Since the parabola opens upwards, the vertex represents a minimum point.

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