The correct match for the graphs for each of the following equations are:
y = (x + 4)² - 3 → 1st graph;
y = (x + 5) (x - 1) → 4th graph;
y = -x² - 3x - 5 → correct graph is 1st image below
y = - (x -1)² -1 → correct graph is 2nd image below.
The graph of a quadratic equation.
The graph of a quadratic equation gives a shape of a parabola or a U-shaped curve. The direction of the parabola can open in an upward or downward direction depending on the sign of the coefficient. The general formula of a quadratic equation is ax² + bx + c = 0.
From the given information, we are match an equation to the correct graph. Using the GeoGebra Calculator to plot out our graphs and starting with the first equation, we have:
y = (x + 4)² - 3
From the graph, the roots of the equation are (-5.73, 0) and (-2,27,0). Thus, the first graph is correct.
y = (x + 5) (x - 1); The roots of the equation are (-5,0) and (1,0). The last graph is a correct.
y = -x² - 3x - 5; The y-intercept of this equation is (0,-5), thus, the correct graph is not part of the listed graphs. The correct graph can be seen in the image below.
y = - (x -1)² -1; The y-intercept of this equation is (0,-2), thus, the correct graph can be seen in the second image attached below.