Complete a table of values for y = x^2 + 2x - 3, identify a point on the graph, and...

Check the final answer first, then review the worked steps.

Problem

Complete a table of values for y = x^2 + 2x - 3, identify a point on the graph, and solve a quadratic equation from the graph.

Answer

a) A = 0 b) Point D c) $x = -3$ and $x = 1$

Step-by-step solution

1. Calculate the value of A: The table provides values for $x$ and $y$ corresponding to the equation $y = x^2 + 2x - 3$. To find the value of A, we need to substitute $x=1$ into the equation.
$$y = (1)^2 + 2(1) - 3$$
$$y = 1 + 2 - 3$$
$$y = 3 - 3$$
$$y = 0$$
So, the value that should replace A is 0.

  1. Identify the point at x=1: We need to find which point (B, C, D, or E) corresponds to $x=1$. From the previous step, we found that when $x=1$, $y=0$. Therefore, we are looking for the point with coordinates $(1, 0)$. Observing the graph, point D is located at $(1, 0)$.
  1. Solve the equation using the graph: To solve the equation $x^2 + 2x - 3 = 0$ using the graph, we need to find the x-intercepts of the graph of $y = x^2 + 2x - 3$. The x-intercepts are the points where the graph crosses the x-axis, which means $y=0$. Looking at the graph, the parabola intersects the x-axis at $x = -3$ and $x = 1$.

Therefore, the solutions to $x^2 + 2x - 3 = 0$ are $x = -3$ and $x = 1$.