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.
What is the Factor Theorem?
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this graph, the roots are [tex]x_1 = 0, x_2 = 4[/tex], 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).
What is the equation of a parabola given it’s vertex?
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 https://brainly.com/question/24737967
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