Match the Quadratic Function y = -6x² to its Corresponding Graph

Question

One function

y=−6x2 y=-6x^2

to the corresponding graph:

1234

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
00:10 We want to find the intersection point with the Y-axis
00:14 Let's substitute X=0 and solve to find the intersection point with the Y-axis
00:17 This is the intersection point with the Y-axis, which is also with the X-axis
00:23 Let's draw the graph according to the function type and the intersection point we found
00:28 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to match the function y=−6x2 y = -6x^2 with its graph. This function represents a downward-opening parabola with the vertex at the origin (0,0)(0,0). The coefficient −6-6 is negative, confirming it opens downwards, and its large absolute value indicates that the parabola closes towards the axis more sharply than a standard y=−x2 y = -x^2 curve.

Let's identify the characteristics of y=−6x2 y = -6x^2 :
- The graph is a parabola, opening downwards.
- The vertex is at the origin, (0,0)(0,0).
- Symmetric around the y-axis.
- Its steepness is greater than the standard parabola y=−x2 y = -x^2 due to the coefficient −6 -6 .

By analyzing the given graph options, the graph marked as 4 aligns perfectly with these properties: It is centered on the origin, opens downwards, and has an evident steep slope.

Therefore, the correct graph that matches the function y=−6x2 y = -6x^2 is option 4.

Answer

4

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Parabola of the Form y=x²+c: Match functions to the appropriate graphs