How do you find the vertex of a quadratic equation?
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Nathaniel Adams
Works at Intel, Lives in Hillsboro, OR
Hello! As an expert in mathematics, I can certainly help you understand how to find the vertex of a quadratic equation. A quadratic equation is typically written in the form \( ax^2 + bx + c = 0 \), where \( a \), \( b \), and \( c \) are constants, and \( x \) is the variable.
The vertex form of a quadratic equation is given by \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola. To find the vertex, you can use the following steps:
1. Identify the coefficients \( a \), \( b \), and \( c \) from the quadratic equation.
2. Calculate the x-coordinate of the vertex using the formula \( h = -\frac{b}{2a} \).
3. Substitute \( h \) back into the original equation to find the y-coordinate \( k \).
4. The vertex \( (h, k) \) is then the point where the parabola changes direction.
Now, let's translate this into Chinese:
大家好！作为数学领域的专家，我可以帮助你理解如何找到二次方程的顶点。二次方程通常以形式 \( ax^2 + bx + c = 0 \) 写成，其中 \( a \)，\( b \) 和 \( c \) 是常数，\( x \) 是变量。
二次方程的顶点形式由 \( y = a(x - h)^2 + k \) 给出，其中 \( (h, k) \) 是抛物线的顶点。要找到顶点，你可以使用以下步骤：
1. 从二次方程中识别出系数 \( a \)，\( b \) 和 \( c \)。
2. 使用公式 \( h = -\frac{b}{2a} \) 计算顶点的 x坐标。
3. 将 \( h \) 代入原方程以找到 y坐标 \( k \)。
4. 然后顶点 \( (h, k) \) 就是抛物线改变方向的点。
The vertex form of a quadratic equation is given by \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola. To find the vertex, you can use the following steps:
1. Identify the coefficients \( a \), \( b \), and \( c \) from the quadratic equation.
2. Calculate the x-coordinate of the vertex using the formula \( h = -\frac{b}{2a} \).
3. Substitute \( h \) back into the original equation to find the y-coordinate \( k \).
4. The vertex \( (h, k) \) is then the point where the parabola changes direction.
Now, let's translate this into Chinese:
大家好！作为数学领域的专家，我可以帮助你理解如何找到二次方程的顶点。二次方程通常以形式 \( ax^2 + bx + c = 0 \) 写成，其中 \( a \)，\( b \) 和 \( c \) 是常数，\( x \) 是变量。
二次方程的顶点形式由 \( y = a(x - h)^2 + k \) 给出，其中 \( (h, k) \) 是抛物线的顶点。要找到顶点，你可以使用以下步骤：
1. 从二次方程中识别出系数 \( a \)，\( b \) 和 \( c \)。
2. 使用公式 \( h = -\frac{b}{2a} \) 计算顶点的 x坐标。
3. 将 \( h \) 代入原方程以找到 y坐标 \( k \)。
4. 然后顶点 \( (h, k) \) 就是抛物线改变方向的点。
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Studied at Harvard University, Lives in Boston. Passionate about environmental conservation and currently working for a non-profit organization.
(The vertex formula is derived from the completing-the-square process, just as is the Quadratic Formula. In each case, memorization is probably simpler than completing the square.) For a given quadratic y = ax2 + bx + c, the vertex (h, k) is found by computing h = �Cb/2a, and then evaluating y at h to find k.
2023-04-15 08:03:58
Oliver Bell
QuesHub.com delivers expert answers and knowledge to you.
(The vertex formula is derived from the completing-the-square process, just as is the Quadratic Formula. In each case, memorization is probably simpler than completing the square.) For a given quadratic y = ax2 + bx + c, the vertex (h, k) is found by computing h = �Cb/2a, and then evaluating y at h to find k.
