Algebra

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the graphing function is shown with two points on each side and one point at the end

a graphing function with an orange line going through the center and two points on it

The parabola opens upward, indicating that the function is a quadratic function with a positive leading coefficient (in this case, the coefficient of the x2 term is 1). The vertex is at (−1,0), and the axis of symmetry is the vertical line x=−1. The y-intercept is at (0,1). Note: The graph is a parabola that opens upward, indicating that the function is a quadratic function with a positive leading coefficient.

a graph that has the slope and range on it, with an arrow pointing up to the

Graphs Of Functions

Finding Slope From A Graph

Graphing Quadratic Functions

Domain And Range

Pair Of Linear Equations In Two Variables

Linear Equations In Two Variables

Real Numbers

The domain of a quadratic function is all real numbers, and the range is all real numbers greater than or equal to the minimum value. Graphing Quadratic Function The graph of a quadratic function is a parabola that opens upward or downward. The vertex, axis of symmetry, and y-intercept can be used to graph the function.

the shape of an upward curve is shown in red and green

Concave Up (U-Shaped) A quadratic function can have a U-shaped curve that opens upward, like a smile. This type of curve is called concave up. The curve starts by falling, then reaches a minimum point (the vertex), and finally rises. The vertex is the lowest point on the curve, and it’s where the function reaches its minimum value. The curve is symmetrical around the vertex, meaning that if you draw a line through the vertex, the two sides of the curve are mirror images of each other.

Y Intercept

The y-intercept of a quadratic function is the point where the parabola intersects the y-axis, and it represents the value of the function when x is equal to 0. To find the y-intercept, set x = 0 and solve for y, which results in the value of the constant term in the quadratic equation, providing a single y-intercept.

an x - intercept is shown in the diagram below

Quadratic Formula

The x-intercept of a quadratic function is the point where the parabola intersects the x-axis, and it represents the solutions to the equation. To find the x-intercept, set y=0 and solve for x, which results in a quadratic equation that can be factored or solved using the quadratic formula, yielding one or two x-intercepts.

a graph with an arrow pointing to the point

Quick Saves

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex of the parabola, dividing it into two mirror images. Its equation is x=−b2a, where a and b are the coefficients of the x2 and x terms, respectively, and it helps to identify the vertex and graph the function.

the graphing function is shown with an arrow pointing to the point

Formula Cans

The vertex of a quadratic function in the form f(x)=ax2+bx+c is: (−b2a, f(−b2a)) This formula can be used to find the vertex of any quadratic function.

Polynomial Functions

Higher Power

A quadratic function is a polynomial function of degree two, which means the highest power of the variable (usually x) is two. It has the general form: f(x)=ax2+bx+c

Logarithmic Functions

Point Slope Form

Distance Formula

The List of Algebric Formulas