QUESTION 15 Find the coordinates for the vertex of the following quadratic function algebraically. Be prepared to show your algebraic work. \( \mathbf{P}(\mathbf{x})=2 \mathrm{x}^{2}-5 \mathbf{x} \) Enter the exact coordinates separately in each blank. (Do not round values.) The vertex is (
Upstudy AI Solution
Answer
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
The Deep Dive
To find the vertex of the quadratic function \( P(x) = 2x^2 - 5x \), we can use the vertex formula, which gives the x-coordinate of the vertex as \( x = -\frac{b}{2a} \). Here, \( a = 2 \) and \( b = -5 \), so: \[ x = -\frac{-5}{2 \times 2} = \frac{5}{4} \] Now, plug this x-coordinate back into the function to find the y-coordinate: \[ P\left(\frac{5}{4}\right) = 2\left(\frac{5}{4}\right)^2 - 5\left(\frac{5}{4}\right) = 2 \cdot \frac{25}{16} - \frac{25}{4} = \frac{50}{16} - \frac{100}{16} = -\frac{50}{16} = -\frac{25}{8} \] Thus, the vertex is \( \left(\frac{5}{4}, -\frac{25}{8}\right) \). The vertex is \( \left( \frac{5}{4}, -\frac{25}{8} \right) \).