Question
1. find the x -intercept about \( y=x^{2}-3 x-4 \)
Ask by Schneider Morgan. in the United Arab Emirates
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
函数 \( y = x^{2} - 3x - 4 \) 的 x 截距是 \( x = -1 \) 和 \( x = 4 \)。
Solution
要求函数 \( y = x^{2} - 3x - 4 \) 的 x 截距，即令 \( y = 0 \)，然后解方程：
\[
0 = x^{2} - 3x - 4
\]
这是一个标准的二次方程，可以使用求根公式来解：
\[
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
\]
其中，\( a = 1 \)，\( b = -3 \)，\( c = -4 \)。
代入数值：
\[
x = \frac{3 \pm \sqrt{(-3)^{2} - 4 \times 1 \times (-4)}}{2 \times 1} = \frac{3 \pm \sqrt{9 + 16}}{2} = \frac{3 \pm \sqrt{25}}{2} = \frac{3 \pm 5}{2}
\]
计算两个解：
\[
x_1 = \frac{3 + 5}{2} = 4
\]
\[
x_2 = \frac{3 - 5}{2} = -1
\]
因此，函数的 x 截距为：
\[
( -1, 0 ) \quad \text{和} \quad (4, 0)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the x-intercept of the equation \(y = x^2 - 3x - 4\), set \(y\) to zero and solve for \(x\): \[ 0 = x^2 - 3x - 4 \] Factoring the quadratic gives you \((x - 4)(x + 1) = 0\). Thus, the x-intercepts are \(x = 4\) and \(x = -1\). So your intercepts are the points \((4, 0)\) and \((-1, 0)\)! Next, let’s remember that finding x-intercepts is like playing hide and seek with the graph! The x-intercepts are where the curve dips below and then pops back above the x-axis, revealing those 'hidden' points! Graphing this equation would show you how it behaves around these intercepts.
