Question

Please Help!

How do I find the X and Y intercept to this equation?

y=-1(x-3)^2+4

Answer 1

\[y=-1(x-3)^{2}+4\]

Answer 2

The X and Y intercepts are:
x=5,1
y=-5

Answer 3

Tell me if you need the steps.

Answer 4

@Blank  The steps would be very helpful

Answer 5

Just a second...

Answer 6

y=-1(x-3)^(2)+4

To find the x-intercept, substitute in 0 for y and solve for x.
(0)=-1(x-3)^(2)+4

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
-1(x-3)^(2)+4=(0)

Squaring an expression is the same as multiplying the expression by itself 2 times.
-((x-3)(x-3))+4=(0)

Multiply -1 by the (x-3)(x-3) inside the parentheses.
-(x-3)(x-3)+4=(0)

Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
-(x*x+x*-3-3*x-3*-3)+4=(0)

Multiply x by x to get x^(2).
-(x^(2)+x*-3-3*x-3*-3)+4=(0)

Multiply x by -3 to get -3x.
-(x^(2)-3x-3*x-3*-3)+4=(0)

Multiply -3 by x to get -3x.
-(x^(2)-3x-3x-3*-3)+4=(0)

Multiply -3 by -3 to get 9.
-(x^(2)-3x-3x+9)+4=(0)

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, x is a factor of both -3x and -3x.
-(x^(2)+(-3-3)x+9)+4=(0)

Subtract 3 from -3 to get -6.
-(x^(2)-6x+9)+4=(0)

Multiply -1 by each term inside the parentheses (x^(2)-6x+9).
(-(x^(2))-(-6x)-(9))+4=(0)

Multiply -1 by the x^(2) inside the parentheses.
(-x^(2)-(-6x)-(9))+4=(0)

Multiply -1 by the -6x inside the parentheses.
(-x^(2)+6x-(9))+4=(0)

Multiply -1 by the 9 inside the parentheses.
-x^(2)+6x-9+4=(0)

Add 4 to -9 to get -5.
-x^(2)+6x-5=(0)

For a polynomial of the form x^(2)+bx+c, find two factors of c (-5) that add up to b (6). In this problem -5*-1=-5 and -5-1=6, so insert -5 as the right hand term of one factor and -1 as the right-hand term of the other factor.
(x-5)(x-1)=(0)

If any individual factor on the left-hand side of the equation is equal to 0, the entire expression will be equal to 0.
(x-5)=0_(x-1)=0

Set the first factor equal to 0 and solve.
x-5=0

Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides.
x=5

Set the next factor equal to 0 and solve.
x-1=0

Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides.
x=1

The final solution is all the values that make (x-5)(x-1)=(0) true.
x=5,1

To find the y-intercept, substitute in 0 for x and solve for y.
y=-1((0)-3)^(2)+4

Any expression with zero in the numerator is zero.
y=-1(0-3)^(2)+4

Adding 0 to an expression does not change the value of the expression.
y=-1(-3)^(2)+4

Squaring an expression is the same as multiplying the expression by itself 2 times.
y=-((-3)(-3))+4

Multiply -3 by -3 to get 9.
y=-(9)+4

Multiply -1 by the 9 inside the parentheses.
y=-9+4

Add 4 to -9 to get -5.
y=-5

These are the x and y intercepts of the equation y=-1(x-3)^(2)+4.
x=5,1, y=-5


Hope this helps. :)

Answer 7

Thank you so much

Answer 8

ǝɯoɔlǝʍ ǝɹ,noʎ :)