Solve these equations. show on a number line. |x-3|=0
1 answer:
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Answer:
<em>Observe attached image</em>
<em>Function zeros:</em>
(3, 0), (5, 0)
<em>Vertex:</em>
(4, 2)
<em>Axis of symmetry:</em>
<em></em>
Step-by-step explanation:
<u>First factorize the function</u>
<em>Take -2 as a common factor.</em>
<em>Now factor the expression </em>
You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.
These numbers are -5 and -3
Then we can factor the expression in the following way:
<em><u>The quadratic function cuts the x-axis at </u></em><em>x = 3 and at x = 5.</em>
Now we find the coordinates of the vertex.
For a function of the form the x coordinate of its vertex is:
In the function
<u>Then the vertice is:</u>
The y coordinate of the symmetry axis is
The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.
<u>Then the axis of symmetry is the line</u>
<u>The solutions and the vertice written as ordered pairs are:</u>
<em>Function zeros:</em>
(3, 0), (5, 0)
<em>Vertex:</em>
(4, 2)
Answer:
Step-by-step explanation:
Triangle P is mapped onto Q so P is the initial triangle that will transformed.
We can rotate counterclockwise 90° but we cannot do it about the origin (0,0) because the red point (5, 1) will end up at ( -1, 5) .
We see that the point (5, 1) ends up at ( -2, 4) so the center of rotation is lower than the origin.
The transformation is rotation of 90° about the point (0,-1)
