Questions: Write an equation (any form) for the quadratic graphed below y=

Solution Steps

The vertex of the parabola is the highest point on the graph. From the graph, the vertex is at (3, 4).

Since we know the vertex, we can use the vertex form of a quadratic equation: \[ y = a(x - h)^2 + k \] where \((h, k)\) is the vertex. Here, \(h = 3\) and \(k = 4\), so the equation becomes: \[ y = a(x - 3)^2 + 4 \]

To find the value of \(a\), we need another point on the graph. From the graph, we can see that the point (2, 3) lies on the parabola. Substitute \(x = 2\) and \(y = 3\) into the equation: \[ 3 = a(2 - 3)^2 + 4 \] \[ 3 = a(-1)^2 + 4 \] \[ 3 = a + 4 \] \[ a = 3 - 4 \] \[ a = -1 \]

Final Answer