What are the x-intercepts of the graph of the quadratic function

Mathematics

1 answer:

Svetllana [295]4 years ago

5 0

Zero Product Property: if a × b = 0, then either a or b = 0 or both a and b = 0.

(Make sure to set f(x) to zero)

So for this equation, I will be factoring by grouping. Firstly, what two terms have a product of -5x^2 and a sum of 4x? That would be 5x and -x. Replace 4x with 5x - x: $0=5x^2+5x-x-1$

Next, factor 5x^2 + 5x and -x - 1 separately. Make sure that they have the same quantity on the inside: $0=5x(x+1)-1(x+1)$

Now you can rewrite the equation as: $0=(5x-1)(x+1)$

Now apply zero product property to the factors to solve for x:

$5x-1=0\\5x=1\\x=\frac{1}{5}\\\\x+1=0\\x=-1$

The x-intercepts are (1/5 ,0) and (-1,0).

You might be interested in

What is the surface area of this shape(step by step if possible)

Genrish500 [490]

Answer:

Step-by-step explanation:

((8 x 10) x 3) + ((9 x 8)/2) x2 = (80 x 3) + (72/2) x 2
= 240 + (36 x 2)
= 240 + 72
= 312

7 0

2 years ago

James is earning money to buy a $100 bike. For each dollar James earns, his mom has agreed to give him $1. So far, he has earned

djyliett [7]

14+7=21 21+21=42 100-42=68

6 0

3 years ago

A circle has the equation 2x²+12x+2y²−16y−150=0.

KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

$(x-h)^{2} +(y-k)^{2}=r^{2}$ (1)

Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

Now, we are given the equation of this circle as follows:

$2x^{2}+12x+2y^{2}-16y-150=0$ (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

$2(x^{2}+6x+y^{2}-8y-75)=0$ (3)

Rearranging the equation:

$x^{2}+6x+y^{2}-8y=75$ (4)

$(x^{2}+6x)+(y^{2}-8y)=75$ (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :