Use the parabola tool to graph the quadratic function f(x)=(x-5)^2+1
1 answer:
Answer:
Look to the attached graph
Step-by-step explanation:
* Lets revise how to graph the quadratic function
- Find the vertex of it
- Find the y-intercept
- Find the x-intercept
∵ f(x) = (x - 5)² + 1 ⇒ the completing square form
- The completing square form for any quadratic is
( x - h)² + k, where h and k are the coordinate of the vertex point
* Lets compare the two forms
∵ (x - h)² + k = (x - 5)² + 1
∴ h = 5 and k = 1
∴ The vertex of the parabola is (5 , 1)
- To find the x-intercept put f(x) = 0
∵ (x - 5)² + 1 = 0 ⇒ subtract 1 from both sides
∴ (x - 5)² = -1 ⇒ the square can not give -ve number
∴ The parabola does not intersect the x-axis
- To find the y-intercept put x = 0
∵ f(0) = (0 - 5)² + 1 = 25 + 1 = 26
∴ The parabola intersects the y-axis at point (0 , 26)
- The parabola is opened upward because the coefficient of x² is +ve
* Now lets graph it
- Look to the attached graph
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Answer:
y = -4x - 6
Step-by-step explanation:
The equation of a line in point-slope form.
is the equation of the line containing point (x1, y1) and having slope, m.
The given point of the perpendicular bisector is (-1, -2), so in this case, x1 = -1, and y1 = -2.
We need the slope of the perpendicular bisector. First we find the slope of the segment. We start at point (-5, -3). We go up 1 unit and 4 units to the right, and we are at another point on the segment. Since slope = rise/run, the slope of the segment is 1/4. The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular bisector is the negative reciprocal of 1/4, so for the perpendicular bisector, m = -4.
Now we use the equation above and our values.