Algebra 1 State Test Prep

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It represents the maximum or minimum value of the function.

Front

How do you find the maximum height of a projectile modeled by a quadratic equation?

Back

Use the formula t = -b/(2a) from the standard form h = at^2 + bt + c, where 'a' and 'b' are coefficients from the equation.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Front

How do you factor a quadratic equation of the form x^2 + bx + c?

Back

Look for two numbers that multiply to 'c' and add to 'b'. These numbers can be used to express the quadratic as (x + m)(x + n) where m and n are the two numbers.

Front

What is the relationship between the coefficients of a quadratic function and its graph?

Back

The coefficients determine the shape, direction, and position of the parabola on the graph.

Front

What does it mean for a function to be in vertex form?

Back

A quadratic function is in vertex form if it is expressed as f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

Front

How do you determine the x-intercepts of a quadratic function?

Back

Set the function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.