Match y=-2x²-3 to its Corresponding Parabola Graph

One function

$y=-2x^2-3$

to the corresponding graph:

Video Solution

Solution Steps

00:00 Match the function to the appropriate graph

00:03 Notice the coefficient of X squared is negative, so the function is concave down

00:11 We want to find the Y-axis intersection point

00:14 Substitute X=0 and solve to find the Y-axis intersection point

00:20 This is the Y-axis intersection point

00:24 Let's draw the graph according to the function type and the intersection point we found

00:30 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll match the given function $y = -2x^2 - 3$ with its corresponding graph based on specific characteristics:

The function $y = -2x^2 - 3$ is a quadratic equation representing a parabola.
Since the coefficient of $x^2$ is negative, the parabola opens downward.
The y-intercept is -3, which means the parabola crosses the y-axis at $-3$ .
The maximum point (vertex) of the parabola occurs at its axis of symmetry, from which we know it opens downward from that point.

Given these observations, we analyze each graphical option:

Graph 1 represents a parabola opening upward, so it does not match.
Graph 2 might have an appropriate direction but not the correct intercept.
Graph 3 doesn't match key features such as y-intercept and direction.
Graph 4 shows a downward opening parabola with its intercept significantly influenced by negative vertical shift, which matches $y = -2x^2 - 3$ .

Therefore, the function $y = -2x^2 - 3$ matches with graph option 4.