x² at the point P and intersects the x-axis at (-15,0) as shown in the Line 1 is tangent to the graph of y = x -- 120 figure above. a. Find the x-coordinates of point P. b. Write an equation for the line l. x2 c. If the line of symmetry for the curve y = x- 120 intersects line l at point R, what is the length of QR ?

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jongun6k jongun6k

22-02-2022
Mathematics

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x² at the point P and intersects the x-axis at (-15,0) as shown in the Line 1 is tangent to the graph of y = x -- 120 figure above. a. Find the x-coordinates of point P. b. Write an equation for the line l. x2 c. If the line of symmetry for the curve y = x- 120 intersects line l at point R, what is the length of QR ?

x at the point P and intersects the xaxis at 150 as shown in the Line 1 is tangent to the graph of y x 120 figure above a Find the xcoordinates of point P b Wri class=

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Medunno13 Medunno13 · Answer 1 · 2022-02-22T20:07:23+01:00

Answer:

Step-by-step explanation:

a) We know that y' = 1 - x/60. This will be the slope of our tangent. However, we also know this tangent has an x-intercept of (-15, 0).

This means that y - 0 = (1 - x/60)(x + 15).

From here you can find the intersection of this line with the parabola.

b) Find the equation of the line passing through (-15, 0) and pt P, nothing too hard

c) The axis of symmetry for the given curve is x=-b/2a = -(1)/(-1/60) = 60. So you need to find the point on line l where x=60, and find the distance from that pt to the vertex