Vertex To Standard Form And Rotation Questions?

1. Given part of an equation of a parabola in vertex form as y = a(x - 8)2 - 2. If this graph passes through the point (4, 6), what is the value of ‘c’ value when the equation is written in standard form?





2. If the coordinates of B are (2, -3), what are the coordinates of B', the image of B after R90° ° ry-axis (B)?


A. (-2, -3)


B. (-3, 2)


C. (-3, -2)


D. (3, -2)

Vertex To Standard Form And Rotation Questions?
Hi,





1. Given part of an equation of a parabola in vertex form as y = a(x - 8)² - 2. If this graph passes through the point (4, 6), what is the value of ‘c’ value when the equation is written in standard form?





If (4,6) is a point on y = a(x - 8)² - 2, we can substitute 4 for x and 6 for y to solve for the value of "a".





y = a(x - 8)² - 2


6 = a(4 - 8)² - 2


6 = a(-4)² - 2


8 = a(-4)²


8 = 16a


½ = a


So the equation is y = ½(x - 8)² - 2


y = ½(x² - 16x + 64) - 2


y = ½x² - 8x + 32 - 2


y = ½x² - 8x + 30 %26lt;== The value of "c" is 30.








2. If the coordinates of B are (2, -3), what are the coordinates of B', the image of B after R90° ° ry-axis (B)?





If I understand your question, the point (2,-3) is to be rotated 90° counterclockwise and then reflected across the y axis.





If you had (2,-3) graphed and put a pencil point at the origin, you could rotate the graph 90° clockwise so the positive x axis would become the positive y axis. The new position of B in the first quadrant would be (3,2). If that point was then reflected across the y axis, it would be located at (-3,2). Consequently, B' would be (-3,2) which is answer B.





A. (-2, -3)


B. (-3, 2) %26lt;== answer


C. (-3, -2)


D. (3, -2)





I hope that helps!! :-)