Question

Solve for the quadratic equations and find the two x-intercepts, find the y-intercept and sketch the graph of the quadratic equation:
y=(x-3)(x+5) and y=(x+1)(x+6)

Answer 1

First, let's solve for the x-intercepts by setting y=0 for each equation:

1. For y=(x-3)(x+5):
0=(x-3)(x+5)
x-3=0 or x+5=0
x=3 or x=-5

Therefore, the x-intercepts are at x=3 and x=-5.

2. For y=(x+1)(x+6):
0=(x+1)(x+6)
x+1=0 or x+6=0
x=-1 or x=-6

Therefore, the x-intercepts are at x=-1 and x=-6.

Next, let's find the y-intercept by setting x=0 for each equation:

1. For y=(x-3)(x+5):
y=(0-3)(0+5)
y=-3*5
y=-15

Therefore, the y-intercept is at y=-15.

2. For y=(x+1)(x+6):
y=(0+1)(0+6)
y=1*6
y=6

Therefore, the y-intercept is at y=6.

Now, let's sketch the graph of each quadratic equation:

1. For y=(x-3)(x+5):
- The x-intercepts are at x=3 and x=-5.
- The y-intercept is at y=-15.
- The graph will intersect the x-axis at x=3 and x=-5, and the y-axis at y=-15.
- The graph will be a parabola opening upwards.

2. For y=(x+1)(x+6):
- The x-intercepts are at x=-1 and x=-6.
- The y-intercept is at y=6.
- The graph will intersect the x-axis at x=-1 and x=-6, and the y-axis at y=6.
- The graph will be a parabola opening upwards.

I recommend graphing these equations on a graphing calculator or software to visualize the exact shape of the parabolas.