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Given the factored form of the function y=(x-4)(x-3), find the following: a.) Find the x-intercepts qquad b.) Find the vertex qquad

Given the factored form of the function \newliney=(x−4)(x−3)y=(x-4)(x-3), find the following:\newlinea.) Find the xx-intercepts\newlineb.) Find the vertex

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Full solution

Q. Given the factored form of the function \newliney=(x−4)(x−3)y=(x-4)(x-3), find the following:\newlinea.) Find the xx-intercepts\newlineb.) Find the vertex
  1. Identify x-intercepts: Identify the x-intercepts by setting y=0y = 0 and solving for xx.y=(x−4)(x−3)=0y = (x-4)(x-3) = 0x−4=0x - 4 = 0 or x−3=0x - 3 = 0x=4x = 4 or x=3x = 3
  2. Calculate vertex: Calculate the vertex using the formula for the vertex of a parabola given in factored form, which is the midpoint of the x-intercepts and the y-value by substituting this x-value back into the equation.\newlineMidpoint of x=4x = 4 and x=3x = 3 is 4+32=3.5\frac{4+3}{2} = 3.5\newliney = (3.5−4)(3.5−3)=(−0.5)(0.5)=−0.25(3.5-4)(3.5-3) = (-0.5)(0.5) = -0.25\newlineVertex = (3.5,−0.25)(3.5, -0.25)

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