Alg 1 Spring Final Review

Front

What is the shape of the graph of the equation Y = -3x^2 + 7x - 2?

Back

The graph is a parabola that opens downwards and is narrower than the parent graph.

Front

What are the 5 Laws of Exponents?

Back

1. Product of Powers: a^m * a^n = a^(m+n)\n2. Quotient of Powers: a^m / a^n = a^(m-n)\n3. Power of a Power: (a^m)^n = a^(m*n)\n4. Power of a Product: (ab)^n = a^n * b^n\n5. Power of a Quotient: (a/b)^n = a^n / b^n

Front

Which equation in vertex form matches the quadratic graph?

Back

The equation is y = (x-3)^2 + 1.

Front

How is the parent function transformed in the equation y = (x-4)^2?

Back

The parent function is shifted right 4 units.

Front

Factor the expression 3a^2 + 4a + 1.

Back

The factored form is (3a+1)(a+1).

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What does the 'a' value in the vertex form indicate about the parabola?

Back

The 'a' value indicates the direction of opening (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x^2.

Front

How do you determine the axis of symmetry for a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation ax^2 + bx + c.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction of opening.