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

Q: Why is the axis of symmetry x = 0 and not x = 7?

The coefficient 7 in $ f(x) = 7x^2 $ makes the parabola narrower, but doesn't shift it left or right. Since there's no bx term (b = 0), the parabola stays centered at the y-axis.

Q: What does 'no linear term' mean in this problem?

A linear term would be something like $ 3x $ or $ -5x $. Since $ f(x) = 7x^2 $ has no x term, b = 0, which keeps the parabola centered at x = 0.

Q: How can I visualize why x = 0 is the axis?

Try plugging in opposite values: $ f(-2) = 7(-2)^2 = 28 $ and $ f(2) = 7(2)^2 = 28 $. Since both give the same y-value, the axis must be halfway between at x = 0!

Q: Does the number 7 affect the axis at all?

No! The coefficient 7 only changes how wide or narrow the parabola looks. It doesn't move the parabola left or right, so the axis stays at x = 0.

Axis of Symmetry with Simple Quadratics

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=7x^2$

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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

00:09 Let's examine the function coefficients

00:18 We'll use the formula to calculate the vertex point

00:28 We'll substitute appropriate values according to the given data and solve for X at the point

00:36 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.

$f(x)=7x^2$

Step-by-step solution

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

Step 1: Identify the coefficients in the quadratic equation.
Step 2: Apply the formula for the axis of symmetry.
Step 3: Substitute the coefficients into the formula and solve.

Now, let's work through each step:
Step 1: The quadratic function given is $f(x) = 7x^2$ which can be written in the form $ax^2 + bx + c$ . Here, $a = 7$ , $b = 0$ , and $c = 0$ .
Step 2: We'll use the formula for the axis of symmetry: $x = -\frac{b}{2a}$ .
Step 3: Substitute $a = 7$ and $b = 0$ in the formula:
$x = -\frac{0}{2 \times 7} = 0$ Therefore, the axis of symmetry for the quadratic function $f(x) = 7x^2$ is $x = 0$ .

Therefore, the solution to the problem is $x = 0$ , corresponding to choice #3.

Final Answer

$x=0$

Key Points to Remember

Essential concepts to master this topic

Formula: Axis of symmetry is $x = -\frac{b}{2a}$ for $ax^2 + bx + c$
Technique: When b = 0, axis becomes $x = -\frac{0}{2a} = 0$
Check: Verify by plotting: $f(-1) = 7$ and $f(1) = 7$ are equal ✓

Common Mistakes

Avoid these frequent errors

Using the coefficient 'a' as the axis of symmetry
Don't think x = 7 because a = 7 in $f(x) = 7x^2$ = wrong axis! The coefficient 'a' affects the parabola's width, not its center. Always use the formula $x = -\frac{b}{2a}$ to find the axis.

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 axis of symmetry x = 0 and not x = 7?

The coefficient 7 in $f(x) = 7x^2$ makes the parabola narrower, but doesn't shift it left or right. Since there's no bx term (b = 0), the parabola stays centered at the y-axis.

What does 'no linear term' mean in this problem?

A linear term would be something like $3x$ or $-5x$ . Since $f(x) = 7x^2$ has no x term, b = 0, which keeps the parabola centered at x = 0.

How can I visualize why x = 0 is the axis?

Try plugging in opposite values: $f(-2) = 7(-2)^2 = 28$ and $f(2) = 7(2)^2 = 28$ . Since both give the same y-value, the axis must be halfway between at x = 0!

Does the number 7 affect the axis at all?

No! The coefficient 7 only changes how wide or narrow the parabola looks. It doesn't move the parabola left or right, so the axis stays at x = 0.

What if the question was f(x) = 7x² + 4?

Adding a constant like +4 moves the parabola up or down, but the axis of symmetry would still be $x = 0$ because there's still no bx term!

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

Axis of Symmetry with Simple 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 = 7?

What does 'no linear term' mean in this problem?

How can I visualize why x = 0 is the axis?

Does the number 7 affect the axis at all?

What if the question was f(x) = 7x² + 4?

🌟 Unlock Your Math Potential

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