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belka [17]
1 year ago
12

35 POINTS please help asap

Mathematics
1 answer:
andrezito [222]1 year ago
7 0

The quadratic equation given in the graph can be represented in these two following ways:

  • Factored: f(x) = 2x(x - 4).
  • Vertex form: y = 2(x - 2)² - 8.

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots x_1, x_2, \codts, x_n is given by:

f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)

In which a is the leading coefficient.

In this graph, the roots are x_1 = 0, x_2 = 4, hence the factored form of the polynomial is:

f(x) = ax(x - 4).

When x = 5, y = 10, hence the leading coefficient is found as follows:

10 = 5a(5 - 4)

5a = 10

a = 2.

Hence the factored form of the polynomial is:

f(x) = 2x(x - 4).

<h3>What is the equation of a parabola given it’s vertex?</h3>

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the vertex is at point (2,-8), hence h = 2, k = -8 and:

y = a(x - 2)² - 8

When x = 5, y = 10, hence the leading coefficient is found as follows:

10 = a(5 - 2)² - 8

9a = 18

a = 2.

Hence the equation in vertex-form is:

y = 2(x - 2)² - 8

More can be learned about quadratic functions at brainly.com/question/24737967

#SPJ1

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