y=-x^2+2x+3

Question

What is the vertex?

What are the coordinates for x-intercept?

what are the coordinates for the  y-intercept?

Answer 1

y  = -x ^2 + 2x + 3

Compare it to standard form of parabola y  = ax ^2 + bx +c.

a = -1 , b = 2 , c = 3.

Axis of symmetry x  = -b / 2a = -2 / 2(-1) = 1

Substitute the x  value in y = -x ^2 + 2x + 3.

y  = -(1)^2 + 2(1) + 3

y  = -1+ 2 + 3

y = 4

Vertex of parabola (x , y )= (1 , 4).

To find y  intercept substitute x  = 0 in y = -x ^2 + 2x + 3.

y  = -(0)^2 + 2(0) + 3

y  = 3

y  intercept is 3.

To find x  intercepts substitute y  = 0 in y  = -x ^2 + 2x + 3.

0 = - x ^2 + 2x + 3

x ^2 - 2x - 3 = 0

x ^2 - 3x + x - 3 = 0

x (x - 3) + 1(x - 3) = 0

(x - 3)(x + 1) = 0

x - 3 = 0 and x + 1 = 0

x = 3 and x = -1.

x  intercepts are 3 and -1.

Vertex of parabola (x , y )= (1 , 4).

Coordinates for y - intercept is (0 , 3)

Coordinates for x - intercepts are (3, 0) and (-1 , 0).