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y=x^(2)+4x-21 The given equation represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the x intercepts of the parabola as constants or coefficients? Choose 1 answer: (A) y=(x-3)(x+7) (B) y=x(x+4)-21 (c) y=(x+2)^(2)-25 (D) y+24=(x+1)(x+3)

y=x2+4x−21 y=x^{2}+4 x-21 \newlineThe given equation represents a parabola in the xy x y -plane. Which of the following equivalent forms of the equation displays the x x intercepts of the parabola as constants or coefficients?\newlineChoose 11 answer:\newline(A) y=(x−3)(x+7) y=(x-3)(x+7) \newline(B) y=x(x+4)−21 y=x(x+4)-21 \newline(C) y=(x+2)2−25 y=(x+2)^{2}-25 \newline(D) y+24=(x+1)(x+3) y+24=(x+1)(x+3)

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Q. y=x2+4x−21 y=x^{2}+4 x-21 \newlineThe given equation represents a parabola in the xy x y -plane. Which of the following equivalent forms of the equation displays the x x intercepts of the parabola as constants or coefficients?\newlineChoose 11 answer:\newline(A) y=(x−3)(x+7) y=(x-3)(x+7) \newline(B) y=x(x+4)−21 y=x(x+4)-21 \newline(C) y=(x+2)2−25 y=(x+2)^{2}-25 \newline(D) y+24=(x+1)(x+3) y+24=(x+1)(x+3)
  1. Factor Quadratic Equation: To find the xx-intercepts of the parabola, we need to factor the quadratic equation if possible. The given equation is y=x2+4x−21y = x^2 + 4x - 21. We will look for two numbers that multiply to −21-21 and add up to 44.
  2. Identify Correct Factored Form: The two numbers that satisfy these conditions are 77 and −3-3 because 7×(−3)=−217 \times (-3) = -21 and 7+(−3)=47 + (-3) = 4. Therefore, we can factor the quadratic equation as y=(x−3)(x+7)y = (x - 3)(x + 7).
  3. Confirm Matching Choice (A): Now we will check the answer choices to see which one matches the factored form of the equation. The factored form should directly show the xx-intercepts as constants or coefficients.
  4. Review Other Choices: Choice (A) y=(x−3)(x+7)y = (x - 3)(x + 7) matches the factored form we found, which displays the xx-intercepts of the parabola as constants or coefficients. The xx-intercepts are x=3x = 3 and x=−7x = -7.
  5. Choice (B) Analysis: We will quickly review the other choices to confirm that they do not display the xx-intercepts in the same clear manner as choice (A).
  6. Choice (C) Analysis: Choice (B) y=x(x+4)−21y = x(x + 4) - 21 does not display the xx-intercepts as constants or coefficients in a factored form.
  7. Choice (D) Analysis: Choice (C) y=(x+2)2−25y = (x + 2)^2 - 25 is in vertex form and does not display the xx-intercepts as constants or coefficients.
  8. Choice (D) Analysis: Choice (C) y=(x+2)2−25y = (x + 2)^2 - 25 is in vertex form and does not display the xx-intercepts as constants or coefficients.Choice (D) y+24=(x+1)(x+3)y + 24 = (x + 1)(x + 3) is not in the standard form of a quadratic equation and does not display the xx-intercepts as constants or coefficients.

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