Finding the Axis of Symmetry: Solve for Symmetry in f(x) = 4x^2 + 6

Q: What does it mean when there's no x term in the middle?

When there's no x term (like in $ f(x) = 4x^2 + 6 $), it means the coefficient b = 0. This creates a perfect vertical symmetry around the y-axis!

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

Because b = 0 in our function! Using the formula $ x = -\frac{b}{2a} = -\frac{0}{2(4)} = 0 $. When b = 0, the parabola is perfectly centered on the y-axis.

Q: Does the constant term affect the axis of symmetry?

No! The constant c only moves the parabola up or down. The axis of symmetry depends only on coefficients a and b in the formula $ x = -\frac{b}{2a} $.

Axis of Symmetry with Zero Linear Term

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=4x^2+6$

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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

00:10 Let's examine the function coefficients

00:16 We'll use the formula to calculate the vertex point

00:22 We'll substitute appropriate values according to the given data and solve for X at the point

00:29 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.

$f(x)=4x^2+6$

Step-by-step solution

To find the axis of symmetry for the quadratic function $f(x) = 4x^2 + 6$ , we employ the formula for the axis of symmetry of a parabola given by $ax^2 + bx + c$ , which is $x = -\frac{b}{2a}$ .

Given $f(x) = 4x^2 + 0x + 6$ , we identify the coefficients from the function:

$a = 4$
$b = 0$

Substituting these values into the formula:

$x = -\frac{b}{2a} = -\frac{0}{2 \times 4} = 0$

Thus, the axis of symmetry for the quadratic function is $x = 0$ .

Therefore, the solution to the problem is $\mathbf{x = 0}$ .

Final Answer

$x=0$

Key Points to Remember

Essential concepts to master this topic

Formula: Use $x = -\frac{b}{2a}$ for standard form quadratics
Technique: When b = 0, axis becomes $x = -\frac{0}{2a} = 0$
Check: Verify by testing equal distances: f(-1) = 10, f(1) = 10 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the linear coefficient is zero
Don't look for a visible x term when it's missing = using wrong values for b! When no x term appears, b = 0, not undefined. Always identify b = 0 in functions like $4x^2 + 6$ and apply the formula correctly.

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

What does it mean when there's no x term in the middle?

When there's no x term (like in $f(x) = 4x^2 + 6$ ), it means the coefficient b = 0. This creates a perfect vertical symmetry around the y-axis!

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

Because b = 0 in our function! Using the formula $x = -\frac{b}{2a} = -\frac{0}{2(4)} = 0$ . When b = 0, the parabola is perfectly centered on the y-axis.

How can I double-check that x = 0 is correct?

Test equal distances from the axis! Pick any value like x = 2: $f(2) = 4(2)^2 + 6 = 22$ . Then try x = -2: $f(-2) = 4(-2)^2 + 6 = 22$ . Same result means correct axis!

What if I mistakenly used a = 6 instead of a = 4?

You'd get the wrong formula setup! Always identify coefficients from standard form $ax^2 + bx + c$ . Here: a = 4 (coefficient of $x^2$ ), b = 0, c = 6 (constant term).

Does the constant term affect the axis of symmetry?

No! The constant c only moves the parabola up or down. The axis of symmetry depends only on coefficients a and b in the formula $x = -\frac{b}{2a}$ .

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Finding the Axis of Symmetry: Solve for Symmetry in f(x) = 4x^2 + 6

Axis of Symmetry with Zero Linear Term

❤️ 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 does it mean when there's no x term in the middle?

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

How can I double-check that x = 0 is correct?

What if I mistakenly used a = 6 instead of a = 4?

Does the constant term affect the axis of symmetry?

🌟 Unlock Your Math Potential

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