291,917 views
27 votes
27 votes
Standard to Graphing Form: y= -4x^2+48x-149 into graphing form.

Please give step by step

User Yannik Suhre
by
2.6k points

1 Answer

28 votes
28 votes

To put the equation y = -4x^2 + 48x - 149 into graphing form, you will need to complete the square. Here is a step-by-step process:

Begin by factoring out the coefficient of the x^2 term. In this case, the coefficient is -4, so you will need to factor out a -4:

y = (-4)(x^2) + 48x - 149

Next, you will need to add and subtract a value in order to complete the square. The value you add and subtract should be equal to the square of half of the coefficient of the x term. In this case, the coefficient of the x term is 48, so you will need to add and subtract (48/2)^2 = 144:

y = (-4)(x^2 + (48/2)^2 - (48/2)^2) + 48x - 149

Simplify the expression inside the parentheses:

y = (-4)(x^2 + 144 - 144) + 48x - 149

Simplify the expression inside the parentheses:

y = (-4)(x^2) + 48x - 149

Rearrange the terms so that the x^2 term is on the left side and the constant term is on the right side:

x^2 - 12x - 37 = 0

Factor the quadratic equation:

(x - 7)(x + 5) = 0

The solutions to the equation are x = 7 and x = -5. These are the x-coordinates of the points where the graph of the equation intersects the x-axis.

To plot these points on the graph, you will need to substitute each value of x into the original equation and solve for y. For example, if x = 7, then y = (-4)(7^2) + 48(7) - 149 = 25. Similarly, if x = -5, then y = (-4)(-5^2) + 48(-5) - 149 = -149.

Plot the points (7, 25) and (-5, -149) on the graph. The graph of the equation y = -4x^2 + 48x - 149 will be the parabola that passes through these two points.

User Snoobie
by
3.2k points