Write an equation of a line that passes through the point (-5,3) and is parallel to the line y = -2x + 5.
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Answer:
1. <em>Axis of symmetry</em>: x = 3
2. <em>Vertex:</em> (3,5)
3. <em>Solution of the equation</em>:
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- x-intercepts:
- y-intercept: (0, -4)
Explanation:
<u>1. Equation:</u>
<u>2. </u><em><u>Axis of symmetry:</u></em>
That is the equation of a parabola, whose standard form is:
Where:
The axis of symmetry is the vertical line with equation:
Substitute
Thus, the axis of symmetry is:
<em><u>3. Vertex</u></em>
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The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.
To find the y-xoordinate, substitute this value of x into the equation for y:
Therefore, the vertex is (3, 5)
<u>4. Find the x-intercepts</u>
The x-intercepts are the roots of the equation, which are the points wher y = 0.
Use the quadratic equation:
<u>5. Find the y-intercept</u>
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The y-intercet is the value of y when x=0: