Question

Graph the equation Y =x2+2x - 3

Answer 1

Answer:

Plot the following and connect the dots:

y-intercept: (0, -3)

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

vertex: (-1, -4)

Step-by-step explanation:

To graph an equation, you need some points that are on the graph.

y = x² + 2x - 3

This equation is given in standard form, y = ax² + bx + c.

"c" is the y-intercept, where the graph hits the y-axis.

Since c = -3, one point is:

(0, -3)

a = 1; b = 2; c = -3

y = x² + 2x - 3

Since a = 1, we can factor by breaking down "b".

Find two numbers that add to get "b", and also multiply to get "c".

? + ? = 2

? × ? = -3

Try 3 and -1:

3 + -1 = 2                Correct

3 × -1 = -3               Correct

Split the "b" value into p and q. Use group factoring.

y = x² - x + 3x - 3

Group terms that looks alike.

y = (x² - x) + (3x - 3)

Collect another pair of like terms.

y = x(x - 1) + 3(x - 1)

y = (x - 1)(x + 3)                      This is fully factored. Use this to find the roots.

The roots are the x-intercepts, when y = 0.

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

Split the factors and equate them to 0.

0 = x - 1            0 = x + 3

x = 1                   x = -3

(1, 0)             (-3, 0)

We also need the vertex. Use complete the square.

y = x² + 2x - 3

y = (x² + 2x) - 3           Divide the "b" term by 2, and square. (2/2)² = 1

y = (x² + 2x + 1 - 1) - 3              Add and subtract 1.

y = (x² + 2x + 1) - 1 - 3              Take out the negative.

y = (x² + 2x + 1) - 4               Simplify

Now factor the bracketed expression, just like before.

x² + 2x + 1

? + ? = 2

? × ? = 1

Try 1 and 1:

1 + 1 = 2

1 × 1 = 1

The factored expression is: (x + 1)(x + 1) = (x + 1)²

Put it back into the equation for the graph:

y = (x + 1)² - 4

This is vertex form: y = a(x - h)² + k, where the vertex is (h, k).

(-1, -4)

See the graph below, the blue is the plotted points.