stuck on these

Question

Find the vertex of the parabola

x coordinate = y coordinate =  
Graph this function and estimate the x intercepts to the nearest tenth. Give your answers in order. 
x intercept one = x intercept two = 

 

 

Answer 1

The parabola in vertex form  y = 23(x - 14)²

Write the equation in the form y = ax²  + bx + c.

y = 23(x²  + 196 - 28x)

y = 23x² + 4508 - 644x

y = 23x²- 644x + 4508

Compare it to parabola equation y = ax²  + bx + c.

a = 23, b = - 644, c = 4508

Axis of symmetry x = -b/2a

x = -(-644)/2(23)

x = 644/46

x = 14

Substitute x = 14 in y = 23x² + 4508 - 644x

y = 23(14)² - 644(14) + 4508

y = 0

Vertex of parabola (14, 0)

x coordinate of vertex is 14

y coordinate of vertex is 0.

To find x intercept substitute y = 0 in  y = 23(x - 14)²

23(x - 14)² = 0

(x - 14)² = 0

x - 14 = 0

x = 14

In this case only one xintercept .

x intercept is 14

Graph