Solve y = x²: Finding Points Where y Equals 4

Q: Why are there two points where y = 4?

Because both positive and negative numbers give the same result when squared! Since $ 2^2 = 4 $ and $ (-2)^2 = 4 $, the parabola crosses the line $ y = 4 $ at two points.

Q: How do I know which x-values to try?

Don't guess! Set up the equation $ x^2 = 4 $ and solve algebraically by taking the square root of both sides. This gives you the exact x-values.

Q: What if y was a different number, like 9?

Same process! Set $ x^2 = 9 $, then $ x = \sqrt{9} = 3 $ or $ x = -\sqrt{9} = -3 $. The points would be (3, 9) and (-3, 9).

Q: Why do I write the points as (x, y)?

This is coordinate notation! The first number is the x-coordinate (horizontal position) and the second is the y-coordinate (vertical position). So (2, 4) means "go right 2, up 4."

Q: Can y ever be negative for this parabola?

No! Since $ y = x^2 $ and any number squared is always positive or zero, this parabola never goes below the x-axis. The lowest point is (0, 0).

Quadratic Equations with Square Root Solutions

Given the function:

$y=x^2$

Is there a point for ? $y=4$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and solve

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

00:13 Take the root

00:16 When taking a root there are 2 solutions, positive and negative

00:28 These are the 2 points

00:31 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 function:

$y=x^2$

Is there a point for ? $y=4$ ?

Step-by-step solution

To determine if there is a point on the graph of the parabola $y = x^2$ where $y = 4$ , we need to find values of $x$ that satisfy the equation $x^2 = 4$ .

Let's solve the equation step by step:

Set the equation: $x^2 = 4$ .
Take the square root of both sides to solve for $x$ :
$x = \sqrt{4}$ or $x = -\sqrt{4}$ .
This gives us $x = 2$ or $x = -2$ .

Therefore, the points on the graph where $y = 4$ are $(2, 4)$ and $(-2, 4)$ .

This matches the provided correct answer of $(2, 4)$ and $(-2, 4)$ .

Therefore, the correct solution is the point set $(2, 4)$ and $(-2, 4)$ .

Final Answer

$(2,4)$ $(-2,4)$

Key Points to Remember

Essential concepts to master this topic

Rule: Set $x^2 = 4$ and solve by taking square roots
Technique: $\sqrt{4} = 2$ , so $x = 2$ or $x = -2$
Check: Substitute back: $2^2 = 4$ and $(-2)^2 = 4$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative square root solution
Don't only write x = 2 when solving $x^2 = 4$ = missing half the solution! Since both positive and negative numbers give positive squares, you get incomplete answers. Always write both $x = \sqrt{4}$ and $x = -\sqrt{4}$ .

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

Why are there two points where y = 4?

Because both positive and negative numbers give the same result when squared! Since $2^2 = 4$ and $(-2)^2 = 4$ , the parabola crosses the line $y = 4$ at two points.

How do I know which x-values to try?

Don't guess! Set up the equation $x^2 = 4$ and solve algebraically by taking the square root of both sides. This gives you the exact x-values.

What if y was a different number, like 9?

Same process! Set $x^2 = 9$ , then $x = \sqrt{9} = 3$ or $x = -\sqrt{9} = -3$ . The points would be (3, 9) and (-3, 9).

Why do I write the points as (x, y)?

This is coordinate notation! The first number is the x-coordinate (horizontal position) and the second is the y-coordinate (vertical position). So (2, 4) means "go right 2, up 4."

Can y ever be negative for this parabola?

No! Since $y = x^2$ and any number squared is always positive or zero, this parabola never goes below the x-axis. The lowest point is (0, 0).

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