Finding the Symmetry Point of the Quadratic Function f(x) = 3 - 5x²

Q: Why is the x-coordinate always 0 when there's no x term?

When b = 0 (no linear x term), the parabola is perfectly centered on the y-axis! The formula $ x = -\frac{b}{2a} = -\frac{0}{2a} = 0 $ confirms this.

Q: How do I know if this vertex is a maximum or minimum?

Look at the coefficient of $ x^2 $! Since a = -5 is negative, the parabola opens downward, making (0,3) a maximum point.

Q: What if I wrote the function as f(x) = -5x² + 3 instead?

That's the same function! Whether you write $ 3 - 5x^2 $ or $ -5x^2 + 3 $, you still have a = -5, b = 0, c = 3, so the vertex is still (0,3).

Q: Why is the vertex called the 'symmetry point'?

The vertex is the axis of symmetry for a parabola! Every point on one side has a mirror image on the other side at the same distance from this central line.

Vertex Formula with Standard Form Quadratics

Given the expression of the quadratic function

Finding the symmetry point of the function

$f(x)=3-5x^2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the symmetry point in the function

00:03 The symmetry point is the point where if you fold the parabola in half

00:06 The halves will be equal to each other

00:10 We'll examine the function's coefficients

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

00:24 We'll substitute appropriate values according to the given data and solve for X at the point

00:31 This is the X value at the symmetry point

00:35 Now we'll substitute this X value in the function to find the Y value at the point

00:42 This is the Y value at the symmetry point

00:48 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

Finding the symmetry point of the function

$f(x)=3-5x^2$

Step-by-step solution

To find the symmetry point of the quadratic function $f(x) = 3 - 5x^2$ , we follow these steps:

Identify that the function is in the form $f(x) = ax^2 + bx + c$ , where $a = -5$ , $b = 0$ , and $c = 3$ .
The x-coordinate of the symmetry point, also known as the vertex, is given by the formula $x = -\frac{b}{2a}$ .
Substitute the values: $x = -\frac{0}{2(-5)} = 0$ .
Calculate the y-coordinate by substituting $x = 0$ into the function: $f(0) = 3 - 5(0)^2 = 3$ .
Hence, the symmetry point of the function is $(0, 3)$ .

Therefore, the symmetry point of the function $f(x) = 3 - 5x^2$ is $(0, 3)$ .

Final Answer

$(0,3)$

Key Points to Remember

Essential concepts to master this topic

Vertex Formula: For $ax^2 + bx + c$ , x-coordinate is $-\frac{b}{2a}$
Technique: With b = 0, vertex x-coordinate becomes $-\frac{0}{2(-5)} = 0$
Check: Substitute x = 0: $f(0) = 3 - 5(0)^2 = 3$ gives (0,3) ✓

Common Mistakes

Avoid these frequent errors

Forgetting to find the y-coordinate after calculating x
Don't stop at x = 0 and guess the vertex is (0,0)! This gives the wrong point entirely. Always substitute your x-value back into the original function to find the complete vertex (x,y).

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 the x-coordinate always 0 when there's no x term?

When b = 0 (no linear x term), the parabola is perfectly centered on the y-axis! The formula $x = -\frac{b}{2a} = -\frac{0}{2a} = 0$ confirms this.

How do I know if this vertex is a maximum or minimum?

Look at the coefficient of $x^2$ ! Since a = -5 is negative, the parabola opens downward, making (0,3) a maximum point.

What if I wrote the function as f(x) = -5x² + 3 instead?

That's the same function! Whether you write $3 - 5x^2$ or $-5x^2 + 3$ , you still have a = -5, b = 0, c = 3, so the vertex is still (0,3).

Can I find the vertex without using the formula?

Yes! Since there's no x term, the function is symmetric about the y-axis. The vertex must be at x = 0, and $f(0) = 3$ gives you the y-coordinate directly.

Why is the vertex called the 'symmetry point'?

The vertex is the axis of symmetry for a parabola! Every point on one side has a mirror image on the other side at the same distance from this central line.

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Finding the Symmetry Point of the Quadratic Function f(x) = 3 - 5x²

Vertex Formula with Standard Form 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 x-coordinate always 0 when there's no x term?

How do I know if this vertex is a maximum or minimum?

What if I wrote the function as f(x) = -5x² + 3 instead?

Can I find the vertex without using the formula?

Why is the vertex called the 'symmetry point'?

🌟 Unlock Your Math Potential

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