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f(x)=(x+2)^(2)+3
The function represents a parabola in the 
xy-plane. Which of the following is an equivalent form of 
f in which the 
y-intercept of the graph of 
f appears as a constant or coefficient?
Choose 1 answer:
(A) 
f(x)=x^(2)+4x+3
(B) 
f(x)=x^(2)+4x+7
(c) 
f(x)=(x+1)(x+3)⊣
(D) 
f(x)=(x+2)(x+5)

f(x)=(x+2)2+3 f(x)=(x+2)^{2}+3 \newlineThe function represents a parabola in the xy x y -plane. Which of the following is an equivalent form of f f in which the y y -intercept of the graph of f f appears as a constant or coefficient?\newlineChoose 11 answer:\newline(A) f(x)=x2+4x+3 f(x)=x^{2}+4 x+3 \newline(B) f(x)=x2+4x+7 f(x)=x^{2}+4 x+7 \newline(C) f(x)=(x+1)(x+3) f(x)=(x+1)(x+3) \dashv \newline(D) f(x)=(x+2)(x+5) f(x)=(x+2)(x+5)

Full solution

Q. f(x)=(x+2)2+3 f(x)=(x+2)^{2}+3 \newlineThe function represents a parabola in the xy x y -plane. Which of the following is an equivalent form of f f in which the y y -intercept of the graph of f f appears as a constant or coefficient?\newlineChoose 11 answer:\newline(A) f(x)=x2+4x+3 f(x)=x^{2}+4 x+3 \newline(B) f(x)=x2+4x+7 f(x)=x^{2}+4 x+7 \newline(C) f(x)=(x+1)(x+3) f(x)=(x+1)(x+3) \dashv \newline(D) f(x)=(x+2)(x+5) f(x)=(x+2)(x+5)
  1. Expand and Simplify: To find an equivalent form of the function where the y-intercept is visible, we need to expand the squared term and simplify the expression.\newlinef(x)=(x+2)2+3f(x) = (x+2)^2 + 3\newlineExpand the squared term:\newlinef(x)=(x2+4x+4)+3f(x) = (x^2 + 4x + 4) + 3\newlineCombine like terms:\newlinef(x)=x2+4x+7f(x) = x^2 + 4x + 7
  2. Check Answer Choices: Now, we need to check the answer choices to see which one matches the expanded form of the function.\newline(A) f(x)=x2+4x+3f(x) = x^2 + 4x + 3 (This does not match our expanded form.)\newline(B) f(x)=x2+4x+7f(x) = x^2 + 4x + 7 (This matches our expanded form.)\newline(C) f(x)=(x+1)(x+3)f(x) = (x+1)(x+3) (This is factored form and does not show the y-intercept directly.)\newline(D) f(x)=(x+2)(x+5)f(x) = (x+2)(x+5) (This is factored form and does not show the y-intercept directly.)

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