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y=-(x-5)^(2)+9 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^(2)+10 x-16 (B) y=-(x-8)(x-2) (C) y=-(x-7)(x-3)+5 (D) y=-x(x-10)-16

y=−(x−5)2+9 y=-(x-5)^{2}+9 \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=−x2+10x−16 y=-x^{2}+10 x-16 \newline(B) y=−(x−8)(x−2) y=-(x-8)(x-2) \newline(C) y=−(x−7)(x−3)+5 y=-(x-7)(x-3)+5 \newline(D) y=−x(x−10)−16 y=-x(x-10)-16

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Q. y=−(x−5)2+9 y=-(x-5)^{2}+9 \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=−x2+10x−16 y=-x^{2}+10 x-16 \newline(B) y=−(x−8)(x−2) y=-(x-8)(x-2) \newline(C) y=−(x−7)(x−3)+5 y=-(x-7)(x-3)+5 \newline(D) y=−x(x−10)−16 y=-x(x-10)-16
  1. Set yy to 00: The given equation is y=−(x−5)2+9y = -(x - 5)^2 + 9. To find the xx-intercepts, we need to set yy to 00 and solve for xx.\newline0=−(x−5)2+90 = -(x - 5)^2 + 9
  2. Add squared term: Add (x−5)2(x - 5)^2 to both sides to isolate the squared term.\newline(x−5)2=9(x - 5)^2 = 9
  3. Take square root: Take the square root of both sides to solve for xx. Remember that taking the square root of both sides introduces a plus or minus sign.x−5=±9x - 5 = \pm\sqrt{9}
  4. Solve for x: Since 9\sqrt{9} is 33, we have:\newlinex−5=±3x - 5 = \pm 3
  5. Find solutions for x: Solve for x by adding 55 to both sides of each equation.\newlinex=5±3x = 5 \pm 3
  6. Determine factored form: This gives us two solutions for xx, which are the xx-intercepts of the parabola.x=8x = 8 and x=2x = 2
  7. Identify correct form: Now we need to find the equivalent form of the equation that displays these xx-intercepts as constants or coefficients. The factored form of a quadratic equation y=a(x−r)(x−s)y = a(x - r)(x - s) directly shows the xx-intercepts rr and ss. So we need to find the factored form that has (x−8)(x - 8) and (x−2)(x - 2) as factors.
  8. Identify correct form: Now we need to find the equivalent form of the equation that displays these xx-intercepts as constants or coefficients. The factored form of a quadratic equation y=a(x−r)(x−s)y = a(x - r)(x - s) directly shows the xx-intercepts rr and ss. So we need to find the factored form that has (x−8)(x - 8) and (x−2)(x - 2) as factors.The correct factored form that represents the xx-intercepts 88 and 22 is:\newliney=a(x−r)(x−s)y = a(x - r)(x - s)00
  9. Identify correct form: Now we need to find the equivalent form of the equation that displays these xx-intercepts as constants or coefficients. The factored form of a quadratic equation y=a(x−r)(x−s)y = a(x - r)(x - s) directly shows the xx-intercepts rr and ss. So we need to find the factored form that has (x−8)(x - 8) and (x−2)(x - 2) as factors.The correct factored form that represents the xx-intercepts 88 and 22 is:\newliney=a(x−r)(x−s)y = a(x - r)(x - s)00Comparing this with the answer choices, we see that option (B) matches our factored form.

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