Without drawing a graph, calculate the [tex]$y$[/tex]-intercept for the equation: [tex]$y=x^2+9$[/tex]

To find the y -intercept, set x = 0 in the equation.
Substitute x = 0 into the equation y = x 2 + 9 .
Simplify the equation: y = 0 2 + 9 = 9 .
The y -intercept is 9 ​ .

Explanation

Understanding the Problem The problem asks us to find the y -intercept of the equation y = x 2 + 9 without using a graph. The y -intercept is the point where the graph of the equation intersects the y -axis. This occurs when x = 0 .

Substituting x=0 To find the y -intercept, we substitute x = 0 into the equation y = x 2 + 9 . This gives us: y = ( 0 ) 2 + 9

Solving for y Now we simplify the equation to solve for y :
y = 0 + 9 y = 9

Final Answer Therefore, the y -intercept is 9.


Examples
Imagine you're designing a bridge with a parabolic shape represented by the equation y = x 2 + 9 . The y -intercept tells you the height of the bridge at its center (where x = 0 ). In this case, the bridge is 9 units high at its center. Understanding intercepts helps engineers determine key structural dimensions.

Answered by GinnyAnswer | 2025-07-08

The y -intercept of the equation y = x 2 + 9 is found by substituting x = 0 , which gives y = 9 . Therefore, the y -intercept is 9. This means the graph intersects the y -axis at the point ( 0 , 9 ) .
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Answered by Anonymous | 2025-07-20