Sketch the parabola using the given information.

Question

Vertex (0,-2) 

Point (1,4)

Answer 1

First, we need to find the function using the given information.  We can put this function in vertex form:

 

y = a(x - h)² + k

 

where:

a is the coefficient of the x² term

vertex is the coordinate (h, k)

 

h = 0

k = -2

 

y = a(x + 0)² - 2

 

y = ax² - 2

 

 

Next, we plug in the values of the coordinate point (1, 4) into the equation to find a.

 

4 = a(1)²- 2

 

4 = a - 2

 

6 = a

 

 

The function is

 

y = 6x² - 2

 

 

We are not done yet.  We need to find the x-intercepts and y-intercept to fully sketch this parabola.

 

To find x-intercepts, set y=0 and solve for x.

 

 

0 = 6x² - 2

 

2 = 6x²

 

1 / 3 = x²

 

±√(1 / 3) = x

 

x = -0.577               and           x = 0.577

 

 

The x-intercepts are  (-0.577, 0) and (0.577, 0).

 

 

 

To find the y-intercept, set x=0 and solve for y.

 

The y-intercept is (0, -2).  Same as the vertex.

 

 

Finally, plot the y-intercept, and the x-intercepts on a coordinate system.  Connect these points to get the parabola.