Verify Point (3,36) on Function y = x²: Coordinate Check

Q: What does it mean for a function to 'pass through' a point?

A function passes through a point when that point satisfies the function's equation. The coordinates must make the equation true when you substitute them in.

Q: How do I check if any point is on a quadratic function?

Substitute the x-coordinate into the function equation. If the result equals the y-coordinate, then the point is on the curve!

Q: Why isn't (3,36) on the curve y = x²?

When x = 3, the function gives $ y = 3^2 = 9 $. Since 9 ≠ 36, the point (3,36) is not on the curve. The correct point would be (3,9).

Q: What point would actually be on y = x² if y = 36?

Set $ 36 = x^2 $ and solve: $ x = ±6 $. So the points (6,36) and (-6,36) are both on the curve!

Q: Can I use this method for any function?

Yes! This substitution method works for any function type - linear, quadratic, exponential, etc. Just substitute and check if the equation balances.

Function Evaluation with Point Verification

Does the function $y=x^2$ pass through the point where y = 36 and x = 3?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Does the point exist?

00:03 Let's substitute appropriate values according to the given data, and solve to find the point

00:11 Let's calculate the exponent

00:18 It seems the values don't match

00:23 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

Does the function $y=x^2$ pass through the point where y = 36 and x = 3?

Step-by-step solution

To determine if the function $y = x^2$ passes through the point $(3, 36)$ , we need to verify whether substituting $x = 3$ results in $y = 36$ .

Substitute $x = 3$ into the function:

The function is $y = x^2$ .
Substitute $x = 3$ : $y = 3^2$
Calculate the value: $y = 9$

The calculated value of $y$ when $x = 3$ is $9$ . We compare this value to the given $y = 36$ .

Since $9 \neq 36$ , the function $y = x^2$ does not pass through the point $(3, 36)$ .

Therefore, the correct answer is: No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace x with given value in function equation
Technique: Calculate $3^2 = 9$ and compare with y-coordinate
Check: Verify if calculated y equals given y-coordinate: 9 ≠ 36 ✓

Common Mistakes

Avoid these frequent errors

Assuming the point is on the curve without calculation
Don't just assume (3,36) is on $y = x^2$ because the numbers look reasonable = wrong answer! This skips the crucial verification step. Always substitute the x-value into the function and calculate the actual y-value.

Practice Quiz

Test your knowledge with interactive questions

Complete:

The missing value of the function point:

$$ f(x)=x^2 $$

$$ f(?)=16 $$

FAQ

Everything you need to know about this question

What does it mean for a function to 'pass through' a point?

A function passes through a point when that point satisfies the function's equation. The coordinates must make the equation true when you substitute them in.

How do I check if any point is on a quadratic function?

Substitute the x-coordinate into the function equation. If the result equals the y-coordinate, then the point is on the curve!

Why isn't (3,36) on the curve y = x²?

When x = 3, the function gives $y = 3^2 = 9$ . Since 9 ≠ 36, the point (3,36) is not on the curve. The correct point would be (3,9).

What point would actually be on y = x² if y = 36?

Set $36 = x^2$ and solve: $x = ±6$ . So the points (6,36) and (-6,36) are both on the curve!

Can I use this method for any function?

Yes! This substitution method works for any function type - linear, quadratic, exponential, etc. Just substitute and check if the equation balances.

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