Algebra 1 review

Front

What is the solution to the equation 2x^2 + 7x - 15 = 0?

Back

The solutions are x = -5 and x = 1.5.

Front

How do you factor the quadratic expression 3x^2 - 7x - 6?

Back

The factored form is (3x + 2)(x - 3).

Front

What does it mean for a graph to have a minimum?

Back

A graph has a minimum when the vertex is the lowest point on the graph, indicating the lowest value of the function.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax^2 + bx + c = 0.

Front

What are the steps to solve a system of equations graphically?

Back

1. Graph both equations on the same coordinate plane. 2. Identify the point(s) where the graphs intersect.

Front

What is the discriminant in a quadratic equation, and what does it indicate?

Back

The discriminant is b^2 - 4ac. It indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient of x^2 (a) is positive, the parabola opens upwards; if negative, it opens downwards.

Front

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

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.