Find the equation the graphs given below.

Here are the equations for the given graphs: a) Step 1: Identify key features from the graph. The graph shows a parabola opening downwards. The axis of symmetry is indicated by the dotted line x=2. One x-intercept is clearly marked at x=3. Since the axis of symmetry is x=2 and one x-intercept is x=3, the other x-intercept must be symmetric with respect to x=2. The distance from 2 to 3 is 1, so the other x-intercept is 2-1=1. (Note: The label -3 on the x-axis is inconsistent with the axis of symmetry x=2 and x-intercept x=3. We will proceed with x=1 and x=3 as the x-intercepts.) The general form of a quadratic equation with x-intercepts x_1 and x_2 is y = a(x-x_1)(x-x_2). Step 2: Substitute the x-intercepts into the general form. Using x_1=1 and x_2=3: y = a(x-1)(x-3) Step 3: Find the value of a. The graph shows the parabola passing through the y-axis at a negative value. Assuming the y-intercept is (0,-3) (which is visually plausible and a common value for a to be an integer), substitute this point into the equation: -3 = a(0-1)(0-3) -3 = a(-1)(-3) -3 = 3a a = -1 Step 4: Write the final equation by substituting a=-1 and expanding. y = -1(x-1)(x-3) y = -(x^2 - 3x - x + 3) y = -(x^2 - 4x + 3) y = -x^2 + 4x - 3 The equation for graph a) is y = -x^2 + 4x - 3. b) Step 1: Identify key features from the graph. The graph shows a parabola opening upwards. The vertex is clearly marked at (-1, -4). One x-intercept is marked at x=1. The general form of a quadratic equation with vertex (h,k) is y = a(x-h)^2 + k. Step 2: Substitute the vertex coordinates into the general form. Using h=-1 and k=-4: y = a(x-(-1))^2 + (-4) y = a(x+1)^2 - 4 Step 3: Find the value of a. The graph shows an x-intercept at x=1, so the point (1,0) is on the parabola. Substitute this point into the equation: 0 = a(1+1)^2 - 4 0 = a(2)^2 - 4 0 = 4a - 4 4a = 4 a = 1 Step 4: Write the final equation by substituting a=1 and expanding. y = 1(x+1)^2 - 4 y = (x^2+2x+1) - 4 y = x^2+2x-3 The equation for graph b) is y = x^2 + 2x - 3. Send me the next one 📸