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

Q: Why is there a negative sign in the axis formula?

The negative sign comes from completing the square! When we rewrite $ 2x^2 + 8x + 4 $ as $ 2(x + 2)^2 - 4 $, the vertex is at $ x = -2 $.

Q: What if the coefficient 'a' is negative?

The formula $ x = -\frac{b}{2a} $ still works perfectly! Just be extra careful with your negative signs when substituting values.

Q: How can I check if my axis is correct?

Pick two points equal distance from your axis and calculate f(x). If $ f(axis-1) = f(axis+1) $, your axis is right!

Q: Does this work for all quadratic functions?

Yes! The formula $ x = -\frac{b}{2a} $ works for any quadratic in standard form $ ax^2 + bx + c $, whether a is positive or negative.

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

The axis of symmetry is just the x-coordinate (like x = -2). The vertex is the complete point including y-coordinate: (-2, f(-2)).

Axis of Symmetry with Standard Form

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=2x^2+8x+4$

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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's coefficients

00:24 We'll use the formula to calculate the vertex point

00:30 We'll substitute appropriate values according to the given data and solve for X at the point

00:41 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.

$f(x)=2x^2+8x+4$

Step-by-step solution

To solve this problem, we'll apply the formula for the axis of symmetry of a quadratic function:

Step 1: Recognize the function is $f(x) = 2x^2 + 8x + 4$ .
Step 2: Identify the coefficients: $a = 2$ and $b = 8$ .
Step 3: Use the axis of symmetry formula $x = -\frac{b}{2a}$ .

Now, substituting the values of $a$ and $b$ into the formula:
$x = -\frac{8}{2 \times 2}$ ,
$x = -\frac{8}{4}$ ,
$x = -2$ .

Therefore, the axis of symmetry for the given quadratic function is $x = -2$ .

Final Answer

$x=-2$

Key Points to Remember

Essential concepts to master this topic

Formula: For quadratic $ax^2 + bx + c$ , axis is $x = -\frac{b}{2a}$
Calculation: With a=2, b=8: $x = -\frac{8}{2(2)} = -2$
Verify: Check that f(-3) = f(-1) since both are 1 unit from x=-2 ✓

Common Mistakes

Avoid these frequent errors

Using wrong signs in the axis formula
Don't forget the negative sign in $x = -\frac{b}{2a}$ = getting x=2 instead of x=-2! This gives the wrong direction from the y-axis. Always remember the formula has a negative sign before the fraction.

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 there a negative sign in the axis formula?

The negative sign comes from completing the square! When we rewrite $2x^2 + 8x + 4$ as $2(x + 2)^2 - 4$ , the vertex is at $x = -2$ .

What if the coefficient 'a' is negative?

The formula $x = -\frac{b}{2a}$ still works perfectly! Just be extra careful with your negative signs when substituting values.

How can I check if my axis is correct?

Pick two points equal distance from your axis and calculate f(x). If $f(axis-1) = f(axis+1)$ , your axis is right!

Does this work for all quadratic functions?

Yes! The formula $x = -\frac{b}{2a}$ works for any quadratic in standard form $ax^2 + bx + c$ , whether a is positive or negative.

What's the difference between axis and vertex?

The axis of symmetry is just the x-coordinate (like x = -2). The vertex is the complete point including y-coordinate: (-2, f(-2)).

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

Axis of Symmetry with Standard Form

❤️ 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 there a negative sign in the axis formula?

What if the coefficient 'a' is negative?

How can I check if my axis is correct?

Does this work for all quadratic functions?

What's the difference between axis and vertex?

🌟 Unlock Your Math Potential

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