Please answer and label all parts of the questions y=-x2 -2x +4 a) Write the equation in vertex form b) Find the x-intercept(s) to the nearest tenth c) Find the coordinates of the vertex

Answer 1

y = x²-2x + 4

Need to get this into the parabola vertex form of y= a(x-h)² + k

y = x² -2x +1 + 3 where 4 is split up into 1 + 3

y = (x-1)² + 3, Vertex Form

There is no x-intercept because when y = 0, 0 = x² -2x +1 + 3, then x² -2x +1 = - 3 which has no solution

Answer 2

y = - x² -2x + 4

a. Equation of vertex is y = a (x - h)² + k

So, y = - (x² +2x - 4) = - (x² + 2x + 1 - 1 - 4) When you add 1, you must subtract 1

y = -(x+2x+1 - 5)

y = - (x + 1)² + 5 because x+2x+1 = (x+1)²

The equation of Vertex is y = - (x+1)² + 5

b. Find the x- intercepts to the nearest tenth

y = 0 then -(x+1)² + 5 =0

-(x+1)² = - 5 Subtract 5 both sides

(x+1)² = 5 Divide both sides by -1

x+1 = + 2.2 or - 2.2 Square root both sides, square root of 5 is 2.236

x = -1 + 2.2 or x = -1 - 2.2 Subtract 1 both sides

So, x = 1.2 or x = - 3.2

The x-intercepts are 1.2 and - 3.2

c. Find the Coordinate of the Vertex.

Equation of vertex from a. y = - (x+1)² + 5

The vertex is (h, k)

So, the vertex is (-1,5)