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Chapter 2: Problem 13

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=2 x^{2}-8 x+3$$

Short Answer

Expert verified
The vertex of the given parabola is at (2, -5).

Step by step solution

01

Find the 'a' and 'b' values

From the formula \(f(x) = 2x^2 - 8x + 3\), identify that the value of 'a' is 2 and the value of 'b' is -8.
02

Calculate the x-coordinate of the Vertex

Use the formula \(-b/2a\) to find the x-coordinate of the vertex. Substitute 'a' and 'b' with their identified values, which gives us \(x = -(-8)/(2*2) = 2\).
03

Calculate the y-coordinate of the Vertex

The y-coordinate of the vertex can be found by substitifying the x-coordinate (2) into the function. This means \(f(2) = 2*(2)^2 - 8*2+3 = -5\).
04

Combine to Form Vertex

Combine the x and y coordinates to form the vertex. So, the vertex is (2, -5).

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