What is x intercept of the graph of the function f(x) =x^2-16+64

Step-by-step explanation:

Given the quadratic function  , you need to follow these steps:

 1. You must substitute into the function:

2. Now you need to factor the quadratic equation. Choose two numbers whose sum be -16 and whose product be 64.

These numbers are: -8 and -8.

Since the root appears twice, it is a "Double root". Then:

(5, 0) and (-3, 0)

Step-by-step explanation:

To find the x-intercepts, let's set y = 0.

0 = x² - 2x - 15

0 = (x - 5)(x + 3) -- To factor x² - 2x - 15, we need to find 2 numbers with a sum of -2 and product of -15; these numbers are -5 and 3.

x - 5 = 0 or x + 3 = 0 -- Use ZPP (Zero Product Property)

x = 5, x = -3

8

Step-by-step explanation:

Find the x-intercept of f(x) = x² - 16x + 64

The x-intercept of the function occurs when y=0, which is when the graph touches the x-axis. To find it, factor the equation.

For this function, you do not need to use the quadratic formula.

Note the trinomial in standard form f(x) = ax² + bx + c

f(x) = x² - 16x + 64 looks like a perfect trinomial. Perfect trinomials are a special trinomial that follow a pattern you can use to factor.

You know a trinomial is perfect when two times the square root of the first term and the square root of the last to is equal to the absolute value of the middle term. (It does not matter if "b" is negative or positive).

As an equation:

|bx| = 2 √(ax²) √c

In this equation:

ax² = x²

|bx| = 16x

c = 64

Substitute the values into our equation. Check if left side equals right side (LS = RS).

|bx| = 2 √(ax²) √c

16x = 2 √(x²) √64

16x = 2*x*8

16x = 16x

LS = RS

The equation is a perfect trinomial.

To factor perfect trinomials, use the rule:

ax² ± bx + c = (√(ax²) ± √c)²

Whether the ± in factored form is plus or minus depends on if "b" is positive or negative.

Substitute the function and find the factored form.

f(x) = ax² ± bx + c = (√(ax²) ± √c)²

x² - 16x + 64 = (√(x²) - √64)²   Eliminate reverse operations and simplify

= (x - 8)²    Factored form

To find the x - intercept, make y = 0, because that's when the x-intercept occurs. Isolate "x" in reverse BEDMAS order with reverse operations. (Reverse operations "cancel out" a number because the opposite is done.)

f(x) = (x - 8)²         "f(x)" is the same as "y"

y = (x - 8)²          Substitute "y" for 0

0 = (x - 8)²

√0 = √(x - 8)²    Square root both sides

0 = x - 8

0 + 8 = x - 8 + 8     Add 8 to both sides to cancel out the -8 on the left side

8 = x

x = 8     Writing the variable on the left side is standard formatting

Therefore the x-intercept of f(x) = x² - 16x + 64 is 8.

answer in the picture

see explanation

Step-by-step explanation:

To find the x- intercepts let y = 0, that is

(x - 4)(x + 2) = 0

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 2 = 0 ⇒ x = - 2

x- intercepts are x = - 2 and x = 4

The vertex lies on the axis of symmetry which is located at the midpoint of the x- intercepts, thus

= = 1

Substitute x = 1 into the equation for corresponding value of y

y = (1 - 4)(1 + 2) = - 3 × 3 = - 9

vertex = (1, - 9)

The answer to your question is below

Step-by-step explanation:

Data

function   f(x) = x² + 2x - 8

-See the graph below

1) x-intercepts

We observe in the graph that there are no x-intercepts.

2) y-intercepts

We observe in the graph that the y-intercept is (0, 8). Point A

3) axis of symmetry

The axis of symmetry is the line that divides the parabola into two equal parts. This line is x = -1 (blue line)

4) The vertex is the lowest point of the parabola, this point is (-1, 7)

Point B in the graph.

The x intercepts of the graph of the function is (-9,0) and (4,0).

Step-by-step explanation:

Consider the provided function .

The x intercepts of the graph of a function is the point where y = 0 or f(x) = 0.

Substitute f(x) = 0 in the above equation and solve for x.

Now use the zero product rule: if ab = 0, then either a = 0 or b = 0,

or

or

Hence, the ordered pairs are (-9,0) and (4,0).

Therefore, the x intercepts of the graph of the function is (-9,0) and (4,0).

The x intercepts of the graph of the function is (-9,0) and (4,0).

Step-by-step explanation:

Consider the provided function .

The x intercepts of the graph of a function is the point where y = 0 or f(x) = 0.

Substitute f(x) = 0 in the above equation and solve for x.

Now use the zero product rule: if ab = 0, then either a = 0 or b = 0,

or

or

Hence, the ordered pairs are (-9,0) and (4,0).

Therefore, the x intercepts of the graph of the function is (-9,0) and (4,0).

Vertex:  ( -1 , − 9 )

X intercepts (0,-4)(0,2)

Step-by-step explanation: