Determine the vertex, axis of symmetry, x-intercept, and y -intercept for the equation: y=x2+2x−3 .
You can use this video to help you.
BONUS POINT IF YOU ATTACH A SCREEN SHOT OF YOUR GRAPH :)
To find the vertex, axis of symmetry, x-intercept, and y-intercept of the equation y = x^2 + 2x - 3, we can use the following formulas and methods:
1. Vertex formula: The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of x^2 and x, respectively.
For this equation, a = 1 and b = 2, so the x-coordinate of the vertex is x = -2/(2*1) = -1.
2. Plug the x-coordinate of the vertex into the equation to find the y-coordinate of the vertex.
Using x = -1 in the equation, we have y = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4.
Therefore, the vertex is (-1, -4).
3. Axis of symmetry: The axis of symmetry is a vertical line passing through the vertex. In this case, it is x = -1.
4. x-intercepts: These are the points where the graph intersects the x-axis. To find these, set y = 0 in the equation and solve for x.
Setting y = 0, we have x^2 + 2x - 3 = 0.
Factoring or using the quadratic formula, we find that x = -3 and x = 1.
Therefore, the x-intercepts are (-3, 0) and (1, 0).
5. y-intercept: This is the point where the graph intersects the y-axis. To find this, set x = 0 in the equation and solve for y.
Setting x = 0, we have y = 0^2 + 2(0) - 3 = -3.
Therefore, the y-intercept is (0, -3).
Now, let's plot the graph:
The graph of the equation y = x^2 + 2x - 3 is shown in the attached screenshot.
[Attach screenshot here]