y = mx + b slope(m) = 2/3 (-4,8)...x = -4 and y = 8 sub and find b 8 = 2/3(-4) + b 8 = -8/3 + b 8 + 8/3 = b 24/3 + 8/3 = b 32/3 = b equation is : y = 2/3x + 32/3 or 3y = 2x + 32 when y = 10 3(10) = 2x + 32 30 - 32 = 2x -2 = 2x -2/2 = x -1 = x <=== ================= (9,0)(3,y)...slope = 1/2
y = mx + b slope(m) = 1/2 (9,0)...x = 9 and y = 0 sub and find b 0 = 1/2(9) + b 0 = 9/2 + b -9/2 = b equation is : y = 1/2x - 9/2 or 2y = x - 9 sub in 3 for x and solve for y 2y = 3 - 9 2y = -6 y = -6/2 y = -3 <== ================= (8,7)(11,7)...notice how the y values are the same. This means it is a horizontal line. A horizontal line has a slope of 0. ==================== sorry...not too good with the picture graphs
So the equation of the red graph is already given to us: . I assume you meant the blue graph?
We can use the vertex form: , where is the vertex. (We can ignore because is 1 for this graph.) Remember that the vertex is the maximum or minimum of a parabola and the point that the line of symmetry passes through. For f(x) the vertex is (0,0).
The vertex for is at on the coordinate plane. (4 left, 2 down)
Plug into the vertex form:
The double negative becomes a positive, and then you're done:
