Instructions: Given the quadratic function, state whether the parabola opens up or down, and whether it has a maximum or minimum.y=−2x2+8x−3𝑦=−2𝑥2+8𝑥−3The parabola opens and has a vertex of (( ,, )), which is a value.

The quadratic function given is y = -2x^2 + 8x - 3.

Step 1: Identify the coefficient of x^2. In this case, it is -2.

Step 2: Determine the direction of the parabola. If the coefficient of x^2 is positive, the parabola opens upwards. If it is negative, the parabola opens downwards. In this case, since the coefficient is -2, the parabola opens downwards.

Step 3: Determine whether the parabola has a maximum or minimum. If the parabola opens upwards, it has a minimum. If it opens downwards, it has a maximum. Since our parabola opens downwards, it has a maximum.

Step 4: Find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula -b/2a. In this case, a is -2 and b is 8, so the x-coordinate is -8/(2*-2) = 2.

Step 5: Substitute the x-coordinate of the vertex into the equation to find the y-coordinate. So, y = -2*(2)^2 + 8*2 - 3 = -4 + 16 - 3 = 9.

So, the parabola opens downwards and has a maximum value. The vertex of the parabola is (2, 9).