Multiple choice

Each of the following quadratic equations represents the graph shown. Which equation reveals the exact values of the $x-$intercepts of the graph?

  1. $y=\cfrac{1}{2}(2x-5)(x+1)$
  2. $y=2{x}^{2}-\cfrac{3}{2}x-{5}$
  3. $y={ \left( x-\cfrac { 3 }{ 4 } \right) }^{ 2 }$
  4. $y={ \left( x-\cfrac { 3 }{ 2 } \right) }^{ 2 }-\cfrac{9}{16}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The factored form y = a(x - r1)(x - r2) directly shows the x-intercepts as r1 and r2. Option A is in a form that can be easily factored to show intercepts.

AI explanation

To find the x-intercepts of a graph, we set y to zero. In the factored form y = 1/2(2x - 5)(x + 1), setting y = 0 immediately provides the exact values of the roots as x = 5/2 and x = -1. The other options either represent different functions entirely or provide the roots in completed square form, which hides their exact values. This factored equation is the one that reveals the exact x-intercepts.

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