Solve for the Symmetrical Axis in the Quadratic f(x) = -2x² + 16

Q: Why is the coefficient b equal to 0 in this function?

In $ f(x) = -2x^2 + 16 $, there's no x term (no middle term). The standard form is $ ax^2 + bx + c $, so when there's no x term, b = 0.

Q: What does the axis of symmetry tell me about the parabola?

The axis of symmetry $ x = 0 $ means the parabola is perfectly balanced around the y-axis. Points on either side of x = 0 are mirror images of each other!

Q: What if I got a different answer like x = 8?

Double-check your formula! Remember it's $ x = -\frac{b}{2a} $, not $ x = -\frac{c}{2a} $. The constant term 16 is c, not b. Since b = 0, the axis is at x = 0.

Q: Does every quadratic function have an axis of symmetry?

Yes, absolutely! Every parabola has exactly one axis of symmetry. It's a vertical line that passes through the vertex (highest or lowest point) of the parabola.

Quadratic Functions with Axis of Symmetry

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=-2x^2+16$

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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

00:13 Let's examine the function's coefficients

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

00:26 We'll substitute appropriate values according to the given data and solve for X at the point

00:35 And this is the solution to the problem

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.

$f(x)=-2x^2+16$

Step-by-step solution

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

Step 1: Identify the coefficients $a$ and $b$ .
Step 2: Apply the symmetry axis formula.
Step 3: Simplify the expression to find the solution.

Now, let's work through each step:

Step 1: From the quadratic function $f(x) = -2x^2 + 16$ , we identify the coefficients: $a = -2$ and $b = 0$ .

Step 2: Using the formula for the axis of symmetry, $x = -\frac{b}{2a}$ , we substitute the identified coefficients:

$x = -\frac{0}{2(-2)}$ .

Step 3: Simplifying the expression, we have:

$x = 0$ .

Therefore, the solution to the problem is the axis of symmetry: $x = 0$ .

Final Answer

$x=0$

Key Points to Remember

Essential concepts to master this topic

Formula: Axis of symmetry is x = -b/(2a) for quadratic functions
Technique: From f(x) = -2x² + 16, identify a = -2, b = 0
Check: Substitute x = 0: f(0) = -2(0)² + 16 = 16 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly identifying coefficient b
Don't assume b equals the constant term 16 = wrong axis calculation! The term 16 has no x, so b = 0 in the standard form ax² + bx + c. Always identify coefficients in order: a (x² term), b (x term), c (constant).

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

Why is the coefficient b equal to 0 in this function?

In $f(x) = -2x^2 + 16$ , there's no x term (no middle term). The standard form is $ax^2 + bx + c$ , so when there's no x term, b = 0.

What does the axis of symmetry tell me about the parabola?

The axis of symmetry $x = 0$ means the parabola is perfectly balanced around the y-axis. Points on either side of x = 0 are mirror images of each other!

How can I verify that x = 0 is really the axis of symmetry?

Check that points equidistant from x = 0 have the same y-value. For example: $f(1) = -2(1)^2 + 16 = 14$ and $f(-1) = -2(-1)^2 + 16 = 14$ . Same height!

What if I got a different answer like x = 8?

Double-check your formula! Remember it's $x = -\frac{b}{2a}$ , not $x = -\frac{c}{2a}$ . The constant term 16 is c, not b. Since b = 0, the axis is at x = 0.

Does every quadratic function have an axis of symmetry?

Yes, absolutely! Every parabola has exactly one axis of symmetry. It's a vertical line that passes through the vertex (highest or lowest point) of the parabola.

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Solve for the Symmetrical Axis in the Quadratic f(x) = -2x² + 16

Quadratic Functions with Axis of Symmetry

❤️ 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 coefficient b equal to 0 in this function?

What does the axis of symmetry tell me about the parabola?

How can I verify that x = 0 is really the axis of symmetry?

What if I got a different answer like x = 8?

Does every quadratic function have an axis of symmetry?

🌟 Unlock Your Math Potential

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