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Identify the graph of g(x)=4x^(2)+24 x+38.

Identify the graph of \newlineg(x)=4x2+24x+38g(x)=4x^{2}+24x+38.

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Find the vertex of the transformed functionright chevron icon

Full solution

Q. Identify the graph of \newlineg(x)=4x2+24x+38g(x)=4x^{2}+24x+38.
  1. Identify standard form: Identify the standard form of the quadratic equation. \newlineg(x)=4x2+24x+38g(x) = 4x^2 + 24x + 38 is already in the form ax2+bx+cax^2 + bx + c.\newlineHere, a=4a = 4, b=24b = 24, and c=38c = 38.
  2. Calculate x-coordinate: Calculate the x-coordinate of the vertex using the formula x=−b2ax = -\frac{b}{2a}.\newlinex=−242×4=−248=−3x = -\frac{24}{2 \times 4} = -\frac{24}{8} = -3.
  3. Substitute xx into g(x)g(x): Substitute x=−3x = -3 back into g(x)g(x) to find the y-coordinate of the vertex.\newlineg(−3)=4(−3)2+24(−3)+38=4⋅9−72+38=36−72+38=2g(-3) = 4(-3)^2 + 24(-3) + 38 = 4\cdot 9 - 72 + 38 = 36 - 72 + 38 = 2.

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