Question Video: Given the Graph of a Quadratic Function Identify the Maximum or Minimum | Nagwa Question Video: Given the Graph of a Quadratic Function Identify the Maximum or Minimum | Nagwa

# Question Video: Given the Graph of a Quadratic Function Identify the Maximum or Minimum Mathematics • Third Year of Preparatory School

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Consider the quadratic function π(π₯) = π₯Β² β 1. Does the given quadratic function open upward or downward? Does the given quadratic function have a maximum or a minimum value? What is the maximum (or minimum) value of the given quadratic function?

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### Video Transcript

Consider the quadratic function π of π₯ equals π₯ squared minus one. Does the given quadratic function open upward or downward? Does the given quadratic function have a maximum or minimum value? What is the maximum or minimum value of the given quadratic function?

Recall that the shape of a quadratic function is called a parabola, which is a kind of U shape that can either open upward or downward. The graph of the quadratic function π of π₯ equals π₯ squared minus one, as graphed in this image, opens upward. Itβs worth noting here that our quadratic function has been given to us in standard form. Thatβs the forum ππ₯ squared plus ππ₯ plus π. For a quadratic function in this form, if π is greater than zero, the parabola will open upward. In this case, we have an π value of one.

It follows from parabolas that open upward that they will have a minimum value. We can see this on the graph. If we look at the minimum point of this graph, itβs located at zero, negative one. The minimum value of the function will be the minimum output, and thatβs the line that weβve sketched here π¦ equal to negative one.

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