Find the Vertex y=2x^2+3x-7

Problem

y=2*x2+3*x−7

Solution

1. Identify the coefficients a b and c from the quadratic equation in standard form y=a*x2+b*x+c

a=2

b=3

c=−7

2. Calculate the x-coordinate of the vertex using the formula x=−b/(2*a)

x=−3/(2*(2))

x=−3/4

3. Substitute the x-coordinate back into the original equation to find the y-coordinate.

y=2*(−3/4)2+3*(−3/4)−7

4. Simplify the expression to determine the value of y

y=2*(9/16)−9/4−7

y=9/8−18/8−56/8

y=−65/8

Final Answer

Vertex=(−3/4,−65/8)

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