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olga_2 [115]
3 years ago
15

Graph f(x)= -(x-2)²+4

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Mathematics
1 answer:
Mandarinka [93]3 years ago
7 0

Answer: See the graph attached.

Step-by-step explanation:

The standard form of a quadratic function is:

f(x)=a(x-h)+k

Where (h,k) is the vertex of the parabola.

If a is negative, then the parabola opens down.

Then, for the function:

f(x)=-(x-2)^2+4

You can identify:

h=2\\k=4

Then the  vertex of the parabola is at (2,4)

Note that a=-1, therefore the parabola opens down.

Find the intersection with the x-axis. Substitute f(x)=0 and solve for x:

0=-(x-2)^2+4\\0=x^2-4x\\0=x(x-4)\\\\x_1=0\\x_2=4

Knowing that the vertex is at (2,4), the parabola opens down and it intersects the x-axis at x=0 and x=4, you can graph the function, as you observe in the figure attached.

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Step-by-step explanation:

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