need help asap thank you!

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? Use complete sentences.

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

Answer 1

x^2 +2x -3 complete the square, add and subtract 1

(x+1)^2 -3 -1

= (x+1)^2 -4

axis of symmetry is x=-1, vertex is the minimum point (-1,-4) of the upward opening parabola

y intercept = -3 or the point (0,-3)

x intercepts are the zeros

0=x^2+2x -3

x = -1 + or - (1/2)sqr(4+12) = -1 + or -2 = 1 or -3 or the points (1,0) and (-3,0) the x intercepts are equidistant from the x coordinate of the vertex

-b/2a = -1 = x coordinate of the vertex and x=-b/2a = the axis of symmetry

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

distance from -1 to 1 is 2 and from -1 to -3 is 2

The parabola is symmetrical. about -b/2a. Left side y values = right side y values.