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Studying Algebra 1
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Answer 1

K...

Answer 2

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Answer 3

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Answer 4

The lowest or highest point of a parabola is called the vertex.
The x-coordinate of the vertex is found using the formula x = -b/2a
.
To find the y-coordinate of the vertex, substitute the x-coordinate into the equation and solve for y.
The axis of symmetry of a parabola is also found using the formula x =-b/2a

.
Domain is the set of all possible x-values for an equation.
Range is the set of all possible y-values for an equation.
The average rate of change is calculated by dividing the change in the y-values by the change in the x-values.
f(x + k) shifts the graph left if k > 0 and right if k < 0.
f(x) + k shifts the graph up if k > 0 and down if k < 0
f(kx) makes the parabola wider if 0 < |k| < 1, and narrower if |k| > 1. If k is negative, the parabola will open downward.
Remember that f(x) and y are interchangeable.
Completing the Square
Be sure that the equation is equal to f(x) or equal to zero.

Step 1: Separate the constant term from the variable terms.

Step 2: Factor out the leading coefficient (if necessary)

Step 3: Divide the coefficient of the x-term by 2 and square the result.

Step 4: Add the result from step 3 inside the parentheses, and subtract it from the constant term outside the parentheses to keep the equation balanced.

Step 5: Factor the trinomial, and combine the constant terms.
Vertex form
f(x) = a(x − h)2 + k
When h > 0, the graph shifts right h units. When h < 0, the graph shifts left h units. Remember, this applies because it is in (x − h) form.

When k > 0, the graph shifts up k units. When k < 0, the graph shifts down k units.

The vertex is at (h, k)
Solving a quadratic equation from vertex form:
Isolate the squared term.
Raise both sides of the equation to the power of
1/2
(Take the square root).
Solve the two equations to identify the x-intercepts.
Review It
When solving a quadratic equation using the Quadratic Formula:
Write the equation in standard form: ax2+bx+c=0.
Identify the coefficients a, b, and c.
Substitute these values into the Quadratic Formula x=
−b
+
−
√b2−4ac
2a
Simplify each part of the formula step by step, being mindful of the signs.
Rewrite the equation as two separate equations.
If the radicand is not a perfect square, approximate each solution.

Remember:
If the radicand (number under the square root symbol) is a perfect square, you will have two exact, rational solutions. The quadratic equation could have been solved by factoring.
If the radicand is zero, you will have two identical, rational solutions. This quadratic expression is a perfect square trinomial and could have been solved by factoring.
If the radicand is negative, there are no real solutions.
Review It
To solve a real-world problem using a quadratic equation, first translate the information, then solve the equation, and last, check your solution.
Solve projectile problems using the projectile equation: H(t) = −16t2 + vt + s, where H(t) is the current height (in feet) of the object at any time after it is thrown, t is the time (in seconds) the object has been in the air, v is the starting velocity, and s is the starting height.
To solve a quadratic equation using graphing technology, set the equation equal to y. Type the quadratic equation into the graphing technology, and find the points where the parabola crosses the x-axis. These x-intercepts are the solutions to the equation.
Normal Distribution
Standardizing a raw score (finding a z-score) z = x-p/delta
Use the z-score to look up the probability on the table. The probability given in the table is always the area to the left of the z-score.
Solving Non-Linear Systems of Equations
Algebraically:
Use substitution to write a new equation. Solve the resulting quadratic equation through factoring, completing the square, or using the quadratic formula.
Graphically:
Graph both equations, and use technology to find the point of intersection.
The point of intersection on the graph is the solution to the system of equations.
Graphing Radical Equations
Use technology to graph the equation. Add parentheses in the numerator and denominator.
Set the denominator equal to zero and solve the equation to identify the vertical asymptote.
Set the numerator equal to zero and solve the equation to identify the zeros of the function.
Inspect the graph to identify the horizontal asymptote.
Solving Radical Equations
When solving a proportion, the cross products are equal. Solve the resulting equation, and check the solution in the original problem. A solution that does not work in the original problem is an extraneous solution.
Remainder Theorem
The remainder theorem states that when the opposite of the constant from the binomial divisor is substituted into a function for x, the result is the remainder. f(a) is equal to the remainder when the function f(x) is divided by the binomial (x − a).

Answer 5

i need someone to make sure that i know this...

Answer 6

Okay

Answer 7

Okay so what is your question?

Answer 8

i need someone to study with me