Rewrite each quadratic equation in the form ax^2+bx+c=0. Then,use technology to solve each by graphing. ROund you answers to the nearest hundredth, where necessary.
a) 3x^2+30 = -19x
Answer: 3x^2+19x+30 Roots: x = -3
b) 6x^2= 25x-24
Answer: -6x^2+25x-24=0 Roots: x = 1.5
c) -33-23x=4x^2
Answer: 4x^2+23x+33 = 0 Roots: x=-2.75
Thanks!
It is considered "better form" to have your quadratics start with a positive x^2 term
So for #2, I would write:
6x^2 - 25x + 24 = 0 , (just switch all the signs, like multiplying by -1)
Each of your roots satisfy your equations, but each of your quads should have a second root.
Since I don't know which "technology" you are using, I don't know where you went wrong.
Thank you. I was using a TI-83 Calculator
sbs
To rewrite each quadratic equation in the form ax^2+bx+c=0, we need to rearrange the terms so that all the terms are on one side of the equation and the other side is equal to 0.
a) Original equation: 3x^2+30 = -19x
Rearrange the terms: 3x^2 + 19x + 30 = 0
Now the equation is in the form ax^2 + bx + c = 0.
b) Original equation: 6x^2 = 25x - 24
Rearrange the terms: 6x^2 - 25x + 24 = 0
Now the equation is in the form ax^2 + bx + c = 0.
c) Original equation: -33 - 23x = 4x^2
Rearrange the terms: 4x^2 + 23x + 33 = 0
Now the equation is in the form ax^2 + bx + c = 0.
To solve these quadratic equations using technology, we can graph them and find the x-intercepts, which are the solutions or roots of the equation. Let's use a graphing calculator or any online graphing tool.
a) Graph the equation: y = 3x^2 + 19x + 30
Find the x-intercept(s) of the graph, which are the solutions.
The graph intersects the x-axis at x = -3.
Therefore, the roots are x = -3.
b) Graph the equation: y = 6x^2 - 25x + 24
Find the x-intercept(s) of the graph, which are the solutions.
The graph intersects the x-axis at x = 1.5.
Therefore, the roots are x = 1.5.
c) Graph the equation: y = 4x^2 + 23x + 33
Find the x-intercept(s) of the graph, which are the solutions.
The graph intersects the x-axis at x = -2.75.
Therefore, the roots are x = -2.75.
Remember to round your answers to the nearest hundredth if necessary.