y= -2( x + 3)( 2x - 5)

Question

Calculate the y-intercept

Calculate the x - intercepts

Calculate the vertex

Sketch graph of y v.s x

without completing the square 

Answer 1

y intercept is obtained by substituting x=0.

 

x-intercepts are OBVIOUSLY -3 and 5/2 because those x values make y=0 (also called roots, or zeros of function)

 

vertex's x value is the average of the x-intercepts.  then plug hat average in for x to get y-coordinate.

[there's also the formula x_vertex = -b/(2a) if quadratic is in standard form.)

 

sketch is done easily from the four points outlined above.

Answer 2

To find the y-intercept, evaluate y when x=0.

 

y-intercept = (0, 30)

 

 

To find the x-intercept, set evaluate x when y=0.

 

x-intercept = (-3, 0) and (5/2, 0)

 

 

To find the vertex, we need to find the x value that makes an axis of symmetry of the parabola.  If we take the average of x-intercepts, we will have our x-coordinate of the vertex.

 

((5/2) - 3) / 2 =  (-1/2) / 2 = -1/4

 

The vertex occurs at x=-1/4.  Now just evaluate y when x=-1/4 to get the y-coordinate of the vertex.

 

vertex = (-1/4, y)

 

 

Then just plot those 4 points on a coordinate grid and connect them to form a parabola.