Discover the Symmetrical Axis in -3x^2 + 3: A Quadratic Analysis

Q: Why is the axis of symmetry x = 0 and not x = 3?

The axis of symmetry depends on the coefficient of x, not the constant term. Since there's no x term in $ f(x) = -3x^2 + 3 $, we have b = 0, making the axis $ x = 0 $.

Q: How can I visualize this parabola?

This parabola opens downward (because a = -3 is negative) with its vertex at (0, 3). It's symmetric about the y-axis, so points like (-2, -9) and (2, -9) are equidistant from the axis.

Q: Does the negative coefficient affect the axis of symmetry?

No! The sign of coefficient a only determines if the parabola opens up or down. The axis formula $ x = -\frac{b}{2a} $ works the same regardless of whether a is positive or negative.

Axis of Symmetry with Simplified Quadratics

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=-3x^2+3$

❤️ 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 Find the axis of symmetry for the function

00:03 The axis of symmetry is the X value at the vertex point

00:06 The point where if you fold the parabola in half, both halves are identical

00:09 Let's look at the function's coefficients

00:21 We'll use the formula to calculate the vertex point

00:32 We'll substitute appropriate values according to the given data and solve for X at the point

00:43 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

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=-3x^2+3$

Step-by-step solution

To find the axis of symmetry for the quadratic function $f(x) = -3x^2 + 3$ , we follow these steps:

Identify coefficients: Here, $a = -3$ , $b = 0$ , and $c = 3$ .
Use the axis of symmetry formula for a quadratic $ax^2 + bx + c$ given by $x = -\frac{b}{2a}$ .
Substitute $b = 0$ and $a = -3$ into the formula: $x = -\frac{0}{2 \times (-3)}$ .
This simplifies to $x = 0$ .

The axis of symmetry for the quadratic function $f(x) = -3x^2 + 3$ is therefore $x = 0$ .

Final Answer

$x=0$

Key Points to Remember

Essential concepts to master this topic

Formula: Use $x = -\frac{b}{2a}$ for standard form $ax^2 + bx + c$
Technique: When b = 0, the axis becomes $x = -\frac{0}{2a} = 0$
Check: Verify symmetry: $f(-1) = f(1) = 0$ confirms $x = 0$ is correct ✓

Common Mistakes

Avoid these frequent errors

Forgetting the coefficient b equals zero
Don't assume b = 1 when there's no x term = wrong axis calculation! Missing that b = 0 in $f(x) = -3x^2 + 3$ leads to incorrect substitution in the formula. Always identify all coefficients: a = -3, b = 0, c = 3 before using $x = -\frac{b}{2a}$ .

Practice Quiz

Test your knowledge with interactive questions

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$$ f(x)=-3x^2+3 $$

FAQ

Everything you need to know about this question

Why is the axis of symmetry x = 0 and not x = 3?

The axis of symmetry depends on the coefficient of x, not the constant term. Since there's no x term in $f(x) = -3x^2 + 3$ , we have b = 0, making the axis $x = 0$ .

How can I visualize this parabola?

This parabola opens downward (because a = -3 is negative) with its vertex at (0, 3). It's symmetric about the y-axis, so points like (-2, -9) and (2, -9) are equidistant from the axis.

What if the quadratic has an x term?

When there's an x term, b ≠ 0, so you'll get a different axis. For example, in $f(x) = -3x^2 + 6x + 3$ , the axis would be $x = -\frac{6}{2(-3)} = 1$ .

Does the negative coefficient affect the axis of symmetry?

No! The sign of coefficient a only determines if the parabola opens up or down. The axis formula $x = -\frac{b}{2a}$ works the same regardless of whether a is positive or negative.

How do I check if my axis is correct?

Pick two points equidistant from your axis and verify they give the same y-value. For $x = 0$ : try x = -1 and x = 1. Both give $f(-1) = f(1) = 0$ !

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function 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

Discover the Symmetrical Axis in -3x^2 + 3: A Quadratic Analysis

Axis of Symmetry with Simplified Quadratics

❤️ 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

Why is the axis of symmetry x = 0 and not x = 3?

How can I visualize this parabola?

What if the quadratic has an x term?

Does the negative coefficient affect the axis of symmetry?

How do I check if my axis is correct?

🌟 Unlock Your Math Potential

More Questions

Symmetry

Identify the Symmetrical Axis in the Quadratic: 2x^2 + 8x + 4

Determining the Axis of Symmetry in the Quadratic Function 7x^2