Identify the Axis of Symmetry for f(x) = -3x^2 + 12

Q: What's the difference between vertex and axis of symmetry?

The vertex is a point with coordinates like (0,12), while the axis of symmetry is a vertical line like x = 0. The vertex sits ON the axis of symmetry!

Q: Why is b = 0 in this function?

In $ f(x) = -3x^2 + 12 $, there's no x term (no linear term). This means b = 0 in the standard form $ ax^2 + bx + c $.

Q: How do I know the vertex is the highest or lowest point?

Look at the coefficient of $ x^2 $! Since a = -3 is negative, the parabola opens downward, so the vertex (0,12) is the maximum point.

Q: What if the question asked for just the axis of symmetry?

Then your answer would be x = 0 (the vertical line), not the point (0,12). Always read carefully to see if they want the line or the point!

Q: Can I use completing the square instead?

Yes! Since $ f(x) = -3x^2 + 12 = -3(x^2) + 12 = -3(x-0)^2 + 12 $, you can see the vertex is (0,12) directly from vertex form.

Quadratic Vertex with Zero Coefficient

Given the expression of the quadratic function

Finding the symmetry point of the function

$f(x)=-3x^2+12$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the point of symmetry in the function

00:03 The point of symmetry is the point where if you fold the parabola in half

00:06 The halves will be equal to each other

00:09 Let's examine the function's coefficients

00:12 We'll use the formula to calculate the vertex point

00:16 We'll substitute appropriate values according to the given data and solve for X at the point

00:23 This is the X value at the point of symmetry

00:31 Now we'll substitute this X value in the function to find the Y value at the point

00:39 This is the Y value at the point of symmetry

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

Finding the symmetry point of the function

$f(x)=-3x^2+12$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given coefficients from $f(x) = ax^2 + bx + c$ : $a = -3$ , $b = 0$ , and $c = 12$ .
Step 2: Apply the vertex formula $x = -\frac{b}{2a}$ to find the x-coordinate of the vertex.
Step 3: Plug the x-coordinate back into the function to find the y-coordinate.

Now, let's work through each step:
Step 1: The function is given as $f(x) = -3x^2 + 12$ . We have $a = -3$ , $b = 0$ , and $c = 12$ .
Step 2: Using the formula $x = -\frac{b}{2a}$ , substitute $b = 0$ and $a = -3$ :
$x = -\frac{0}{2 \times -3} = 0$
Step 3: Substitute $x = 0$ back into the quadratic function to find the y-coordinate:
$f(0) = -3(0)^2 + 12 = 12$
So, the vertex, or symmetry point, of the function is $(0, 12)$ .

Therefore, the solution to the problem is $(0, 12)$ .

Final Answer

$(0,12)$

Key Points to Remember

Essential concepts to master this topic

Vertex Formula: Use $x = -\frac{b}{2a}$ to find x-coordinate
Technique: When b = 0, vertex x-coordinate equals $-\frac{0}{2(-3)} = 0$
Check: Substitute x = 0: $f(0) = -3(0)^2 + 12 = 12$ ✓

Common Mistakes

Avoid these frequent errors

Confusing axis of symmetry with vertex point
Don't say "the axis of symmetry is (0,12)" = wrong answer format! The axis of symmetry is a vertical line (x = 0), while the vertex is the point (0,12). Always identify what the question asks for - line or point.

Practice Quiz

Test your knowledge with interactive questions

Given the expression of the quadratic function

Finding the symmetry point of the function

$$ f(x)=-5x^2+10 $$

FAQ

Everything you need to know about this question

What's the difference between vertex and axis of symmetry?

The vertex is a point with coordinates like (0,12), while the axis of symmetry is a vertical line like x = 0. The vertex sits ON the axis of symmetry!

Why is b = 0 in this function?

In $f(x) = -3x^2 + 12$ , there's no x term (no linear term). This means b = 0 in the standard form $ax^2 + bx + c$ .

How do I know the vertex is the highest or lowest point?

Look at the coefficient of $x^2$ ! Since a = -3 is negative, the parabola opens downward, so the vertex (0,12) is the maximum point.

What if the question asked for just the axis of symmetry?

Then your answer would be x = 0 (the vertical line), not the point (0,12). Always read carefully to see if they want the line or the point!

Can I use completing the square instead?

Yes! Since $f(x) = -3x^2 + 12 = -3(x^2) + 12 = -3(x-0)^2 + 12$ , you can see the vertex is (0,12) directly from vertex form.

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Identify the Axis of Symmetry for f(x) = -3x^2 + 12

Quadratic Vertex with Zero Coefficient

❤️ 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

What's the difference between vertex and axis of symmetry?

Why is b = 0 in this function?

How do I know the vertex is the highest or lowest point?

What if the question asked for just the axis of symmetry?

Can I use completing the square instead?

🌟 Unlock Your Math Potential

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