Features of Graphs of Quadratic Equations Practice

Question

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Question
Determine the zeros of the quadratic function y=x2+15x+36
. (When listing the smaller zero, remember that negative values are always smaller than positive values.)(1 point)
smaller zero: x=
; greater zero: x=
Remaining Attempts : 3
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Answer 1

To find the zeros of the quadratic function \( y = x^2 + 15x + 36 \), we need to solve for \( x \) when \( y = 0 \). This involves solving the equation:

\[ x^2 + 15x + 36 = 0 \]

We can use the factoring method. We need two numbers that multiply to \( 36 \) and add up to \( 15 \). The numbers \( 3 \) and \( 12 \) meet this criterion:

\[ (x + 3)(x + 12) = 0 \]

Setting each factor to zero gives us:

1. \( x + 3 = 0 \) → \( x = -3 \)
2. \( x + 12 = 0 \) → \( x = -12 \)

Now we can list the zeros. To follow the instruction of smaller and greater:

• Smaller zero: \( x = -12 \)
• Greater zero: \( x = -3 \)

So:

• Smaller zero: \( x = -12 \)
• Greater zero: \( x = -3 \)