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Question

The quadratic formula can be separated into two parts, as shown:

You are going to interpret the quadratic formula graphically by following the steps below:

a. Graph f(x) = x² + 2x - 3 in a paint program, or by hand. Draw the axis of symmetry; label the vertex, and both x-intercepts. When you are finished, you can replace the grid below with your graph.

b. Using the separated quadratic formula, calculate the left term  for f(x) = x² + 2x - 3. Enter your answer below.

c. Compare your answer from part b with your vertex and axis of symmetry in the graph. What do you notice? Use complete sentences.

d. Using the separated quadratic formula, calculate the right term  for f(x) = x² + 2x - 3. Enter your answers below.

e. Looking back at your graph, find the horizontal distance along the x-axis from the vertex to each x-intercept.

f. Compare your answers for parts d and e. What do you notice?

g. Summarize your findings. Explain the relationship between the terms of the quadratic formula and the graph of a quadratic function.

Answer 1

x^2 +2x -3=0 y intercept =-the constant term = -3 or the point (0,-3)

complete the square, add and subtract 1

x^2 +2x + 1 -3 -1=0

(x+1)^2 -4 =0 =(x-h)^2 + k where (h,k) = vertex = (-1,-4)

x+1 = + or - sqr4

x = -1 + or - 2 = 1 or -3

x intercepts are (1,0) and (-3,0)

axis of symmetry is the x coordinate of the midpoint of the x intercepts: (1-3)/2 =-1, x=-1 is the axis of symmetry

x^2 +2x -3

=ax^2 +bx +c with a=1, b=2, c=-3

-b/2a = -2/2(1) = -1 which corresponds to the axis of symmetry, x=-1

+ or -sqr(b^2 -4ac)/2a = + or - sqr(4-4(1)(-3))/2(1) = + or - 2

add and subtract 2 from the x value of the axis of symmetry gives the x intercepts: -1-2=-3 and -1+2 =1

x^2 + 2x -3 = (x+3)(x-1) = 0

x+3=0 x-1=0

x=-3 x=1 are the two x intercepts

the graph is an upward opening parabola with minimum point at the vertex, it's symmetrical around the line x=-1 one y intercept at -3, two x intercepts equidistant from the line of symmetry, x=-3 and x= 1, each 2 from that axis. 2 is the 2nd part of the quadratic formula. the axis of symmetry is the 1st part of the quadratic formula, -b/2a. when a>0, the parabola is upward opening, c= the y intercept