Final answer:
To find the quadratic function that passes through the given points, use the vertex form of a quadratic function. The correct option is f(x) = (3/5)(x + 3/2)^2 - 5/2.
Step-by-step explanation:
To find the quadratic function that passes through the given points, we can use the vertex form of a quadratic function. The vertex form is given by: f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the function. Substituting the given vertex (-3/2, -5/2), we have: f(x) = a(x + 3/2)^2 - 5/2. Now, we can substitute the other given point (1, 55/8) to find the value of a. Plugging in the values, we get: 55/8 = a(1 + 3/2)^2 - 5/2. Solving this equation will give us the value of a.
Cross-multiplying, we have: 55/8 = a(5/2)^2 - 5/2. Simplifying further, we get: 55/8 = 25a/4 - 5/2. Multiplying both sides by 8 to eliminate fractions, we get: 55 = 50a - 20. Adding 20 to both sides, we have: 75 = 50a. Dividing both sides by 50, we find: a = 3/5.
Therefore, the quadratic function that passes through the given points is: f(x) = (3/5)(x + 3/2)^2 - 5/2. Answer choice (a) f(x) = −2x²+3x−1 is not correct.