Algebra STAAR Review - Strategy 4 - Two Line Solving

Front

What is the transformation of the graph of f(x) = x^2 to create h(x) = 2f(x)?

Back

The graph is vertically stretched by a factor of 2.

Front

How do you solve a system of equations by graphing?

Back

Plot both equations on the same graph and identify the point(s) where they intersect.

Front

What value of a makes the equation 0.5(a + 0.5) = -0.25(a + 4) + 2 true?

Back

a = 1.

Front

Given f(x) = 3x + 9, what is f(-4)?

Back

f(-4) = -3.

Front

What are the transformations from the parent function f(x) = x^2 to g(x) = \frac{1}{3}(x - 3)^2 + 6?

Back

The graph becomes wider, shifts right 3 units, and shifts up 6 units.

Front

What does it mean for a function to be 'wider' or 'narrower'?

Back

A function is 'wider' if its graph stretches out more horizontally, and 'narrower' if it compresses vertically.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

Front

How do you find the vertex of a quadratic function in standard form?

Back

Use the formula h = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What does it mean for a system of equations to have an infinite number of solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of y when x = 0.