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

Q: How do I know which way the parabola opens?

Look at the coefficient of x²! If it's positive (like +6x²), the parabola opens upward. If it's negative (like -6x²), it opens downward.

Q: Why is the vertex at (0,0)?

The function $ y = -6x^2 $ has no other terms, so when x = 0, we get y = 0. This makes (0,0) the vertex!

Q: What does the coefficient -6 tell me about the shape?

The absolute value |6| makes the parabola narrower than $ y = -x^2 $. Larger coefficients create steeper, more compressed parabolas.

Q: How can I check if I picked the right graph?

Test a point! Use x = 1: $ y = -6(1)^2 = -6 $. The point (1, -6) should be on your chosen graph.

Q: Are there other points I can use to verify?

x = -1: $ y = -6(-1)^2 = -6 $ gives (-1, -6)x = 2: $ y = -6(2)^2 = -24 $ gives (2, -24)The parabola should be symmetric about the y-axis

Quadratic Functions with Negative Leading Coefficients

One function

$y=-6x^2$

to the corresponding graph:

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

One function

$y=-6x^2$

to the corresponding graph:

Step-by-step solution

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

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

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 $y = -6x^2$ is option 4.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Direction: Negative coefficient means parabola opens downward from vertex
Technique: Use $y = -6x^2$ to find points like $x = 1, y = -6$
Check: Vertex at origin (0,0) and symmetric about y-axis ✓

Common Mistakes

Avoid these frequent errors

Confusing upward and downward opening parabolas
Don't assume all parabolas open upward = wrong graph selection! The negative coefficient -6 is the key indicator. Always check the sign of the coefficient: positive opens up, negative opens down.

Practice Quiz

Test your knowledge with interactive questions

One function

$$ y=-6x^2 $$

to the corresponding graph:

FAQ

Everything you need to know about this question

How do I know which way the parabola opens?

Look at the coefficient of x²! If it's positive (like +6x²), the parabola opens upward. If it's negative (like -6x²), it opens downward.

Why is the vertex at (0,0)?

The function $y = -6x^2$ has no other terms, so when x = 0, we get y = 0. This makes (0,0) the vertex!

What does the coefficient -6 tell me about the shape?

The absolute value |6| makes the parabola narrower than $y = -x^2$ . Larger coefficients create steeper, more compressed parabolas.

How can I check if I picked the right graph?

Test a point! Use x = 1: $y = -6(1)^2 = -6$ . The point (1, -6) should be on your chosen graph.

Are there other points I can use to verify?

x = -1: $y = -6(-1)^2 = -6$ gives (-1, -6)
x = 2: $y = -6(2)^2 = -24$ gives (2, -24)
The parabola should be symmetric about the y-axis

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parabola Families questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

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

Quadratic Functions with Negative Leading Coefficients

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which way the parabola opens?

Why is the vertex at (0,0)?

What does the coefficient -6 tell me about the shape?

How can I check if I picked the right graph?

Are there other points I can use to verify?

🌟 Unlock Your Math Potential

More Questions

Parabola of the Form y=x²+c

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

Match the Function y = -1/2x² + 4 to Its Corresponding Graph

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

Match the Quadratic Function y = x²/4 + 2 to Its Graph