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Sveta_85 [38]
2 years ago
11

Please help y=30x - 30x^2 - 72

Mathematics
1 answer:
Brut [27]2 years ago
3 0

Answer:

  a.  4, 6

  b.  -72

  c.  (5, 3)

  d.  Graph A

Step-by-step explanation:

<h3>a.</h3>

To answer these questions, it is useful to start by factoring the equation.

  y = -3x² +30x -72 . . . . given

  y = -3(x² -10x +24) . . . . factor out leading coefficient

  y = -3(x -4)(x -6)

The x-intercepts are the values of x that make the factors zero:

  x = 4, 6

__

<h3>b.</h3>

The y-intercept is the constant in the equation: -72.

__

<h3>c.</h3>

We know the x-coordinate of the vertex is the midpoint between the x-intercepts: (4+6)/2 = 5. The y-coordinate can be found by evaluating y at that x-value.

  y = -3(5 -4)(5 -6) = -3(1)(-1) = 3

The vertex is (5, 3).

__

<h3>d.</h3>

The graph that has the correct vertex and x-intercepts is Graph A.

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