Complete this table for $y = x^2 + x - 4$ - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

To draw the graph:

1. Plot the points from the completed table on a graph.
2. The points to plot are:
   • (-4, 8)
   • (-3, 2)
   • (-2, -2)
   • (-1, -4)
   • (0, -4)
   • (1, -2)
   • (2, 2)
   • (3, 8)
3. Connect the points to form a parabolic curve, opening upwards, representing the function $y = x^2 + x - 4$.
4. Make sure the graph is labeled with appropriate scales.

To solve $x^2 + x - 4 = 0$ using the graph:

1. Identify the points where the graph intersects the x-axis.
2. From the graph, the intersection points can be found approximately, which represent the solutions of the equation.
3. Let's assume these points intersect at roughly $x ext{ values} = 1.5$ and $x ext{ values} = -3.5$.
4. Hence, the solutions are approximately $x ext{ values} ext{ are } 1.5$ or $-3.5$.

To draw the graph of $y = -2x - 1$:

1. Create a table for $x$ values in the range of $-4$ to $3$.
2. Calculate $y$ for various $x$ values:
   • For $x = -4$, $y = -2(-4) - 1 = 7$
   • For $x = -3$, $y = -2(-3) - 1 = 5$
   • For $x = -2$, $y = -2(-2) - 1 = 3$
   • For $x = -1$, $y = -2(-1) - 1 = 1$
   • For $x = 0$, $y = -1$
   • For $x = 1$, $y = -3$
   • For $x = 2$, $y = -5$
   • For $x = 3$, $y = -7$
3. Plot the points on the same grid as the parabola.
4. Connect the points with a straight line.

To solve $x^2 + x - 4 = -2x - 1$:

1. Rearrange the equation to combine like terms:
   $x^2 + 3x - 3 = 0$.
2. Identify points of intersection between the graphs of $y = x^2 + x - 4$ and $y = -2x - 1$.
3. From the graph, estimate where they intersect, which provides the approximate solutions for the equation.
4. Based on the graph, the intersections can be estimated at points $x = -2$ and $x = 1$.