Find the Axis of Symmetry for the Quadratic Expression -5x^2 - 25x

Q: Why is there no c term in this quadratic?

When there's no constant term, c = 0. This means the parabola passes through the origin (0,0). The axis of symmetry formula $ x = -\frac{b}{2a} $ doesn't need the c value anyway!

Q: How do I convert -2.5 to a mixed number?

Since -2.5 = -2½, think of it as negative two and one-half. The decimal 0.5 equals the fraction ½, so -2.5 becomes $ -2\frac{1}{2} $.

Q: What if I get a positive result instead of negative?

Check your signs carefully! With a = -5 and b = -25, you get $ x = -\frac{(-25)}{2(-5)} = -\frac{-25}{-10} = -\frac{25}{10} = -2.5 $. Double negatives matter!

Q: Can I factor this quadratic to find the axis of symmetry?

Yes! Factor out -5x: $ f(x) = -5x(x + 5) $. The zeros are x = 0 and x = -5, so the axis of symmetry is halfway between: $ x = \frac{0 + (-5)}{2} = -2.5 $.

Q: Why does the axis of symmetry matter?

The axis of symmetry shows you the x-coordinate of the vertex! It's the line where the parabola folds in half, and it helps you graph the function and find maximum or minimum values.

Axis of Symmetry with Standard Formula

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=-5x^2-25x$

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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 look at the function's 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

00:47 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.

$f(x)=-5x^2-25x$

Step-by-step solution

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

Step 1: Identify the given coefficients $a$ and $b$ .
Step 2: Apply the formula for the axis of symmetry.
Step 3: Perform the necessary calculations to find the axis of symmetry.

Now, let's work through each step:
Step 1: The given quadratic function is $f(x) = -5x^2 - 25x$ , so $a = -5$ and $b = -25$ .
Step 2: We'll use the axis of symmetry formula $x = -\frac{b}{2a}$ .
Step 3: Plugging in our values, we get $x = -\frac{-25}{2 \times -5} = -\frac{25}{-10} = -2.5$ .

Therefore, the axis of symmetry for the quadratic $f(x) = -5x^2 - 25x$ is $x = -2\frac{1}{2}$ .

Final Answer

$x=-2\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Formula: Use $x = -\frac{b}{2a}$ for any quadratic function
Technique: From $f(x) = -5x^2 - 25x$ , identify a = -5, b = -25
Check: Substitute x = -2.5 back: vertex should have same y-value on both sides ✓

Common Mistakes

Avoid these frequent errors

Using wrong signs when identifying coefficients
Don't forget the negative sign in front of coefficients like a = -5 and b = -25 = wrong axis calculation! Missing negatives completely changes your formula result. Always carefully identify the sign of each coefficient before applying $x = -\frac{b}{2a}$ .

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

Why is there no c term in this quadratic?

When there's no constant term, c = 0. This means the parabola passes through the origin (0,0). The axis of symmetry formula $x = -\frac{b}{2a}$ doesn't need the c value anyway!

How do I convert -2.5 to a mixed number?

Since -2.5 = -2½, think of it as negative two and one-half. The decimal 0.5 equals the fraction ½, so -2.5 becomes $-2\frac{1}{2}$ .

What if I get a positive result instead of negative?

Check your signs carefully! With a = -5 and b = -25, you get $x = -\frac{(-25)}{2(-5)} = -\frac{-25}{-10} = -\frac{25}{10} = -2.5$ . Double negatives matter!

Can I factor this quadratic to find the axis of symmetry?

Yes! Factor out -5x: $f(x) = -5x(x + 5)$ . The zeros are x = 0 and x = -5, so the axis of symmetry is halfway between: $x = \frac{0 + (-5)}{2} = -2.5$ .

Why does the axis of symmetry matter?

The axis of symmetry shows you the x-coordinate of the vertex! It's the line where the parabola folds in half, and it helps you graph the function and find maximum or minimum values.

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Find the Axis of Symmetry for the Quadratic Expression -5x^2 - 25x

Axis of Symmetry with Standard Formula

❤️ 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 no c term in this quadratic?

How do I convert -2.5 to a mixed number?

What if I get a positive result instead of negative?

Can I factor this quadratic to find the axis of symmetry?

Why does the axis of symmetry matter?

🌟 Unlock Your Math Potential

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