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For the graph of a certain quadratic y = ax^2 + bx + c, the vertex of the parabola is (3,7) and one of the x-intercepts is (-2,0). What is the x-coordinate of the other x-intercept?

Jul 12, 2019

#1
+23354
+3

For the graph of a certain quadratic y = ax^2 + bx + c,
the vertex of the parabola is (3,7) and one of the x-intercepts is (-2,0).
What is the x-coordinate of the other x-intercept?

$$\text{Let x-vertex = x_v = 3 } \\ \text{Let  x-intercept_1 = x_1 = -2 } \\ \text{Let  x-intercept_2 = x_2 =\ ? }$$

$$\begin{array}{|rcll|} \hline \dfrac{x_1+x_2}{2} &=& x_v \\\\ \dfrac{-2+x_2}{2} &=& 3 \quad | \quad \cdot 2 \\\\ -2+x_2 &=& 6 \quad | \quad + 2 \\\\ \mathbf{ x_2 } &=& \mathbf{8} \\ \hline \end{array}$$

The x-coordinate of the other x-intercept is $$\mathbf{ 8 }$$

Jul 12, 2019

#1
+23354
+3

For the graph of a certain quadratic y = ax^2 + bx + c,
the vertex of the parabola is (3,7) and one of the x-intercepts is (-2,0).
What is the x-coordinate of the other x-intercept?

$$\text{Let x-vertex = x_v = 3 } \\ \text{Let  x-intercept_1 = x_1 = -2 } \\ \text{Let  x-intercept_2 = x_2 =\ ? }$$

$$\begin{array}{|rcll|} \hline \dfrac{x_1+x_2}{2} &=& x_v \\\\ \dfrac{-2+x_2}{2} &=& 3 \quad | \quad \cdot 2 \\\\ -2+x_2 &=& 6 \quad | \quad + 2 \\\\ \mathbf{ x_2 } &=& \mathbf{8} \\ \hline \end{array}$$

The x-coordinate of the other x-intercept is $$\mathbf{ 8 }$$

heureka Jul 12, 2019